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Simplifying x(3x + -5) + x(2x + -3) = (5x + 6)(x + -2) Reorder the terms: x(-5 + 3x) + x(2x + -3) = (5x + 6)(x + -2) (-5 * x + 3x * x) + x(2x + -3) = (5x + 6)(x + -2) (-5x + 3x2) + x(2x + -3) = (5x + 6)(x + -2) Reorder the terms: -5x + 3x2 + x(-3 + 2x) = (5x + 6)(x + -2) -5x + 3x2 + (-3 * x + 2x * x) = (5x + 6)(x + -2) -5x + 3x2 + (-3x + 2x2) = (5x + 6)(x + -2) Reorder the terms: -5x + -3x + 3x2 + 2x2 = (5x + 6)(x + -2) Combine like terms: -5x + -3x = -8x -8x + 3x2 + 2x2 = (5x + 6)(x + -2) Combine like terms: 3x2 + 2x2 = 5x2 -8x + 5x2 = (5x + 6)(x + -2) Reorder the terms: -8x + 5x2 = (6 + 5x)(x + -2) Reorder the terms: -8x + 5x2 = (6 + 5x)(-2 + x) Multiply (6 + 5x) * (-2 + x) -8x + 5x2 = (6(-2 + x) + 5x * (-2 + x)) -8x + 5x2 = ((-2 * 6 + x * 6) + 5x * (-2 + x)) -8x + 5x2 = ((-12 + 6x) + 5x * (-2 + x)) -8x + 5x2 = (-12 + 6x + (-2 * 5x + x * 5x)) -8x + 5x2 = (-12 + 6x + (-10x + 5x2)) Combine like terms: 6x + -10x = -4x -8x + 5x2 = (-12 + -4x + 5x2) Add '-5x2' to each side of the equation. -8x + 5x2 + -5x2 = -12 + -4x + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8x + 0 = -12 + -4x + 5x2 + -5x2 -8x = -12 + -4x + 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -8x = -12 + -4x + 0 -8x = -12 + -4x Solving -8x = -12 + -4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4x' to each side of the equation. -8x + 4x = -12 + -4x + 4x Combine like terms: -8x + 4x = -4x -4x = -12 + -4x + 4x Combine like terms: -4x + 4x = 0 -4x = -12 + 0 -4x = -12 Divide each side by '-4'. x = 3 Simplifying x = 3
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