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Simplifying 3(X + -3)(X + -1)(X + -4) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: 3(-3 + X)(X + -1)(X + -4) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: 3(-3 + X)(-1 + X)(X + -4) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: 3(-3 + X)(-1 + X)(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Multiply (-3 + X) * (-1 + X) 3(-3(-1 + X) + X(-1 + X))(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3((-1 * -3 + X * -3) + X(-1 + X))(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3((3 + -3X) + X(-1 + X))(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3(3 + -3X + (-1 * X + X * X))(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3(3 + -3X + (-1X + X2))(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: -3X + -1X = -4X 3(3 + -4X + X2)(-4 + X) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Multiply (3 + -4X + X2) * (-4 + X) 3(3(-4 + X) + -4X * (-4 + X) + X2(-4 + X)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3((-4 * 3 + X * 3) + -4X * (-4 + X) + X2(-4 + X)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3((-12 + 3X) + -4X * (-4 + X) + X2(-4 + X)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3(-12 + 3X + (-4 * -4X + X * -4X) + X2(-4 + X)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3(-12 + 3X + (16X + -4X2) + X2(-4 + X)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3(-12 + 3X + 16X + -4X2 + (-4 * X2 + X * X2)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 3(-12 + 3X + 16X + -4X2 + (-4X2 + X3)) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: 3X + 16X = 19X 3(-12 + 19X + -4X2 + -4X2 + X3) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: -4X2 + -4X2 = -8X2 3(-12 + 19X + -8X2 + X3) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 (-12 * 3 + 19X * 3 + -8X2 * 3 + X3 * 3) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 (-36 + 57X + -24X2 + 3X3) + 2(X + -2)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + 2(-2 + X)(X + -1)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + 2(-2 + X)(-1 + X)(X + -4) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + 2(-2 + X)(-1 + X)(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Multiply (-2 + X) * (-1 + X) -36 + 57X + -24X2 + 3X3 + 2(-2(-1 + X) + X(-1 + X))(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2((-1 * -2 + X * -2) + X(-1 + X))(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2((2 + -2X) + X(-1 + X))(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2(2 + -2X + (-1 * X + X * X))(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2(2 + -2X + (-1X + X2))(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: -2X + -1X = -3X -36 + 57X + -24X2 + 3X3 + 2(2 + -3X + X2)(-4 + X) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Multiply (2 + -3X + X2) * (-4 + X) -36 + 57X + -24X2 + 3X3 + 2(2(-4 + X) + -3X * (-4 + X) + X2(-4 + X)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2((-4 * 2 + X * 2) + -3X * (-4 + X) + X2(-4 + X)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2((-8 + 2X) + -3X * (-4 + X) + X2(-4 + X)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2(-8 + 2X + (-4 * -3X + X * -3X) + X2(-4 + X)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2(-8 + 2X + (12X + -3X2) + X2(-4 + X)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2(-8 + 2X + 12X + -3X2 + (-4 * X2 + X * X2)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + 2(-8 + 2X + 12X + -3X2 + (-4X2 + X3)) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: 2X + 12X = 14X -36 + 57X + -24X2 + 3X3 + 2(-8 + 14X + -3X2 + -4X2 + X3) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: -3X2 + -4X2 = -7X2 -36 + 57X + -24X2 + 3X3 + 2(-8 + 14X + -7X2 + X3) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + (-8 * 2 + 14X * 2 + -7X2 * 2 + X3 * 2) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + (-16 + 28X + -14X2 + 2X3) + -4(X + -2)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-2 + X)(X + -3)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-2 + X)(-3 + X)(X + -4) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-2 + X)(-3 + X)(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 Multiply (-2 + X) * (-3 + X) -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-2(-3 + X) + X(-3 + X))(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4((-3 * -2 + X * -2) + X(-3 + X))(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4((6 + -2X) + X(-3 + X))(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(6 + -2X + (-3 * X + X * X))(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(6 + -2X + (-3X + X2))(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: -2X + -3X = -5X -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(6 + -5X + X2)(-4 + X) + -1(X + -2)(X + -3)(X + -1) = 0 Multiply (6 + -5X + X2) * (-4 + X) -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(6(-4 + X) + -5X * (-4 + X) + X2(-4 + X)) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4((-4 * 6 + X * 6) + -5X * (-4 + X) + X2(-4 + X)) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4((-24 + 6X) + -5X * (-4 + X) + X2(-4 + X)) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-24 + 6X + (-4 * -5X + X * -5X) + X2(-4 + X)) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-24 + 6X + (20X + -5X2) + X2(-4 + X)) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-24 + 6X + 20X + -5X2 + (-4 * X2 + X * X2)) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-24 + 6X + 20X + -5X2 + (-4X2 + X3)) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: 6X + 20X = 26X -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-24 + 26X + -5X2 + -4X2 + X3) + -1(X + -2)(X + -3)(X + -1) = 0 Combine like terms: -5X2 + -4X2 = -9X2 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + -4(-24 + 26X + -9X2 + X3) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + (-24 * -4 + 26X * -4 + -9X2 * -4 + X3 * -4) + -1(X + -2)(X + -3)(X + -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + (96 + -104X + 36X2 + -4X3) + -1(X + -2)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-2 + X)(X + -3)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-2 + X)(-3 + X)(X + -1) = 0 Reorder the terms: -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-2 + X)(-3 + X)(-1 + X) = 0 Multiply (-2 + X) * (-3 + X) -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-2(-3 + X) + X(-3 + X))(-1 + X) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1((-3 * -2 + X * -2) + X(-3 + X))(-1 + X) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1((6 + -2X) + X(-3 + X))(-1 + X) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(6 + -2X + (-3 * X + X * X))(-1 + X) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(6 + -2X + (-3X + X2))(-1 + X) = 0 Combine like terms: -2X + -3X = -5X -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(6 + -5X + X2)(-1 + X) = 0 Multiply (6 + -5X + X2) * (-1 + X) -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(6(-1 + X) + -5X * (-1 + X) + X2(-1 + X)) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1((-1 * 6 + X * 6) + -5X * (-1 + X) + X2(-1 + X)) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1((-6 + 6X) + -5X * (-1 + X) + X2(-1 + X)) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-6 + 6X + (-1 * -5X + X * -5X) + X2(-1 + X)) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-6 + 6X + (5X + -5X2) + X2(-1 + X)) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-6 + 6X + 5X + -5X2 + (-1 * X2 + X * X2)) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-6 + 6X + 5X + -5X2 + (-1X2 + X3)) = 0 Combine like terms: 6X + 5X = 11X -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-6 + 11X + -5X2 + -1X2 + X3) = 0 Combine like terms: -5X2 + -1X2 = -6X2 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + -1(-6 + 11X + -6X2 + X3) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + (-6 * -1 + 11X * -1 + -6X2 * -1 + X3 * -1) = 0 -36 + 57X + -24X2 + 3X3 + -16 + 28X + -14X2 + 2X3 + 96 + -104X + 36X2 + -4X3 + (6 + -11X + 6X2 + -1X3) = 0 Reorder the terms: -36 + -16 + 96 + 6 + 57X + 28X + -104X + -11X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: -36 + -16 = -52 -52 + 96 + 6 + 57X + 28X + -104X + -11X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: -52 + 96 = 44 44 + 6 + 57X + 28X + -104X + -11X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: 44 + 6 = 50 50 + 57X + 28X + -104X + -11X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: 57X + 28X = 85X 50 + 85X + -104X + -11X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: 85X + -104X = -19X 50 + -19X + -11X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: -19X + -11X = -30X 50 + -30X + -24X2 + -14X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: -24X2 + -14X2 = -38X2 50 + -30X + -38X2 + 36X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: -38X2 + 36X2 = -2X2 50 + -30X + -2X2 + 6X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: -2X2 + 6X2 = 4X2 50 + -30X + 4X2 + 3X3 + 2X3 + -4X3 + -1X3 = 0 Combine like terms: 3X3 + 2X3 = 5X3 50 + -30X + 4X2 + 5X3 + -4X3 + -1X3 = 0 Combine like terms: 5X3 + -4X3 = 1X3 50 + -30X + 4X2 + 1X3 + -1X3 = 0 Combine like terms: 1X3 + -1X3 = 0 50 + -30X + 4X2 + 0 = 0 50 + -30X + 4X2 = 0 Solving 50 + -30X + 4X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -15X + 2X2) = 0 Factor a trinomial. 2((5 + -2X)(5 + -1X)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2X)' equal to zero and attempt to solve: Simplifying 5 + -2X = 0 Solving 5 + -2X = 0 Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2X = 0 + -5 -2X = 0 + -5 Combine like terms: 0 + -5 = -5 -2X = -5 Divide each side by '-2'. X = 2.5 Simplifying X = 2.5Subproblem 2
Set the factor '(5 + -1X)' equal to zero and attempt to solve: Simplifying 5 + -1X = 0 Solving 5 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1X = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1X = 0 + -5 -1X = 0 + -5 Combine like terms: 0 + -5 = -5 -1X = -5 Divide each side by '-1'. X = 5 Simplifying X = 5Solution
X = {2.5, 5}
| 3(4y-3)-4=4(5y-6)+7 | | 32-t=-1 | | 15-4x+17=12 | | 5.910-1.708= | | 6(2x+2)=-22 | | 8F-3-6=8f-3f+2+4 | | 3x+y^2=4 | | 4(y+4)=2(y+3) | | w^3-8= | | 5.91-1.708= | | 6n-1+18=4 | | 4x+3y+2=7x+14 | | 3(4g+6)=2(6g+g) | | 3x+6-2x=7+2x-5 | | .2x-.8x-47=1 | | 3c-4c=5c-3c+2 | | 2t-5=6y-1 | | 6k+10=110 | | 1n-7n=18 | | 5y-7=-13i | | (x^3+6x^2-4x+7)-(3x^2+2x-4)= | | 9(a-4)+2(a-20)=a-11 | | u-3=-5u+13 | | 5x+6x-8x=6+6 | | x+x-20=100 | | -4*(x-7)=2x+4 | | 5z-3=2z+12 | | 6*19= | | -3y-5=1-2y | | 8x+12-20x=5-6x-3 | | 6y+6(y-4)= | | x-3x-9=27 |