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Simplifying 3(x + -1(1)) + 5(x + -1(1))(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Multiply -1 * 1 3(x + -1) + 5(x + -1(1))(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Reorder the terms: 3(-1 + x) + 5(x + -1(1))(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 (-1 * 3 + x * 3) + 5(x + -1(1))(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 (-3 + 3x) + 5(x + -1(1))(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Multiply -1 * 1 -3 + 3x + 5(x + -1)(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Reorder the terms: -3 + 3x + 5(-1 + x)(x + -1(3)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Multiply -1 * 3 -3 + 3x + 5(-1 + x)(x + -3) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Reorder the terms: -3 + 3x + 5(-1 + x)(-3 + x) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Multiply (-1 + x) * (-3 + x) -3 + 3x + 5(-1(-3 + x) + x(-3 + x)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 -3 + 3x + 5((-3 * -1 + x * -1) + x(-3 + x)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 -3 + 3x + 5((3 + -1x) + x(-3 + x)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 -3 + 3x + 5(3 + -1x + (-3 * x + x * x)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 -3 + 3x + 5(3 + -1x + (-3x + x2)) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Combine like terms: -1x + -3x = -4x -3 + 3x + 5(3 + -4x + x2) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 -3 + 3x + (3 * 5 + -4x * 5 + x2 * 5) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 -3 + 3x + (15 + -20x + 5x2) + (x + -1(1))(x + -1(3))(x + -1(4)) = 0 Multiply -1 * 1 -3 + 3x + 15 + -20x + 5x2 + (x + -1)(x + -1(3))(x + -1(4)) = 0 Reorder the terms: -3 + 3x + 15 + -20x + 5x2 + (-1 + x)(x + -1(3))(x + -1(4)) = 0 Multiply -1 * 3 -3 + 3x + 15 + -20x + 5x2 + (-1 + x)(x + -3)(x + -1(4)) = 0 Reorder the terms: -3 + 3x + 15 + -20x + 5x2 + (-1 + x)(-3 + x)(x + -1(4)) = 0 Multiply -1 * 4 -3 + 3x + 15 + -20x + 5x2 + (-1 + x)(-3 + x)(x + -4) = 0 Reorder the terms: -3 + 3x + 15 + -20x + 5x2 + (-1 + x)(-3 + x)(-4 + x) = 0 Multiply (-1 + x) * (-3 + x) -3 + 3x + 15 + -20x + 5x2 + (-1(-3 + x) + x(-3 + x))(-4 + x) = 0 -3 + 3x + 15 + -20x + 5x2 + ((-3 * -1 + x * -1) + x(-3 + x))(-4 + x) = 0 -3 + 3x + 15 + -20x + 5x2 + ((3 + -1x) + x(-3 + x))(-4 + x) = 0 -3 + 3x + 15 + -20x + 5x2 + (3 + -1x + (-3 * x + x * x))(-4 + x) = 0 -3 + 3x + 15 + -20x + 5x2 + (3 + -1x + (-3x + x2))(-4 + x) = 0 Combine like terms: -1x + -3x = -4x -3 + 3x + 15 + -20x + 5x2 + (3 + -4x + x2)(-4 + x) = 0 Multiply (3 + -4x + x2) * (-4 + x) -3 + 3x + 15 + -20x + 5x2 + (3(-4 + x) + -4x * (-4 + x) + x2(-4 + x)) = 0 -3 + 3x + 15 + -20x + 5x2 + ((-4 * 3 + x * 3) + -4x * (-4 + x) + x2(-4 + x)) = 0 -3 + 3x + 15 + -20x + 5x2 + ((-12 + 3x) + -4x * (-4 + x) + x2(-4 + x)) = 0 -3 + 3x + 15 + -20x + 5x2 + (-12 + 3x + (-4 * -4x + x * -4x) + x2(-4 + x)) = 0 -3 + 3x + 15 + -20x + 5x2 + (-12 + 3x + (16x + -4x2) + x2(-4 + x)) = 0 -3 + 3x + 15 + -20x + 5x2 + (-12 + 3x + 16x + -4x2 + (-4 * x2 + x * x2)) = 0 -3 + 3x + 15 + -20x + 5x2 + (-12 + 3x + 16x + -4x2 + (-4x2 + x3)) = 0 Combine like terms: 3x + 16x = 19x -3 + 3x + 15 + -20x + 5x2 + (-12 + 19x + -4x2 + -4x2 + x3) = 0 Combine like terms: -4x2 + -4x2 = -8x2 -3 + 3x + 15 + -20x + 5x2 + (-12 + 19x + -8x2 + x3) = 0 Reorder the terms: -3 + 15 + -12 + 3x + -20x + 19x + 5x2 + -8x2 + x3 = 0 Combine like terms: -3 + 15 = 12 12 + -12 + 3x + -20x + 19x + 5x2 + -8x2 + x3 = 0 Combine like terms: 12 + -12 = 0 0 + 3x + -20x + 19x + 5x2 + -8x2 + x3 = 0 3x + -20x + 19x + 5x2 + -8x2 + x3 = 0 Combine like terms: 3x + -20x = -17x -17x + 19x + 5x2 + -8x2 + x3 = 0 Combine like terms: -17x + 19x = 2x 2x + 5x2 + -8x2 + x3 = 0 Combine like terms: 5x2 + -8x2 = -3x2 2x + -3x2 + x3 = 0 Solving 2x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + -3x + x2) = 0 Factor a trinomial. x((1 + -1x)(2 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {0, 1, 2}
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