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Simplifying (x + -1)(3x + 4) + -2(x + -1)(x + 2) = 0 Reorder the terms: (-1 + x)(3x + 4) + -2(x + -1)(x + 2) = 0 Reorder the terms: (-1 + x)(4 + 3x) + -2(x + -1)(x + 2) = 0 Multiply (-1 + x) * (4 + 3x) (-1(4 + 3x) + x(4 + 3x)) + -2(x + -1)(x + 2) = 0 ((4 * -1 + 3x * -1) + x(4 + 3x)) + -2(x + -1)(x + 2) = 0 ((-4 + -3x) + x(4 + 3x)) + -2(x + -1)(x + 2) = 0 (-4 + -3x + (4 * x + 3x * x)) + -2(x + -1)(x + 2) = 0 (-4 + -3x + (4x + 3x2)) + -2(x + -1)(x + 2) = 0 Combine like terms: -3x + 4x = 1x (-4 + 1x + 3x2) + -2(x + -1)(x + 2) = 0 Reorder the terms: -4 + 1x + 3x2 + -2(-1 + x)(x + 2) = 0 Reorder the terms: -4 + 1x + 3x2 + -2(-1 + x)(2 + x) = 0 Multiply (-1 + x) * (2 + x) -4 + 1x + 3x2 + -2(-1(2 + x) + x(2 + x)) = 0 -4 + 1x + 3x2 + -2((2 * -1 + x * -1) + x(2 + x)) = 0 -4 + 1x + 3x2 + -2((-2 + -1x) + x(2 + x)) = 0 -4 + 1x + 3x2 + -2(-2 + -1x + (2 * x + x * x)) = 0 -4 + 1x + 3x2 + -2(-2 + -1x + (2x + x2)) = 0 Combine like terms: -1x + 2x = 1x -4 + 1x + 3x2 + -2(-2 + 1x + x2) = 0 -4 + 1x + 3x2 + (-2 * -2 + 1x * -2 + x2 * -2) = 0 -4 + 1x + 3x2 + (4 + -2x + -2x2) = 0 Reorder the terms: -4 + 4 + 1x + -2x + 3x2 + -2x2 = 0 Combine like terms: -4 + 4 = 0 0 + 1x + -2x + 3x2 + -2x2 = 0 1x + -2x + 3x2 + -2x2 = 0 Combine like terms: 1x + -2x = -1x -1x + 3x2 + -2x2 = 0 Combine like terms: 3x2 + -2x2 = 1x2 -1x + 1x2 = 0 Solving -1x + 1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-1 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {0, 1}
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