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Simplifying (x + 2)(3x + -4) = (x + -2)(2x + 1) Reorder the terms: (2 + x)(3x + -4) = (x + -2)(2x + 1) Reorder the terms: (2 + x)(-4 + 3x) = (x + -2)(2x + 1) Multiply (2 + x) * (-4 + 3x) (2(-4 + 3x) + x(-4 + 3x)) = (x + -2)(2x + 1) ((-4 * 2 + 3x * 2) + x(-4 + 3x)) = (x + -2)(2x + 1) ((-8 + 6x) + x(-4 + 3x)) = (x + -2)(2x + 1) (-8 + 6x + (-4 * x + 3x * x)) = (x + -2)(2x + 1) (-8 + 6x + (-4x + 3x2)) = (x + -2)(2x + 1) Combine like terms: 6x + -4x = 2x (-8 + 2x + 3x2) = (x + -2)(2x + 1) Reorder the terms: -8 + 2x + 3x2 = (-2 + x)(2x + 1) Reorder the terms: -8 + 2x + 3x2 = (-2 + x)(1 + 2x) Multiply (-2 + x) * (1 + 2x) -8 + 2x + 3x2 = (-2(1 + 2x) + x(1 + 2x)) -8 + 2x + 3x2 = ((1 * -2 + 2x * -2) + x(1 + 2x)) -8 + 2x + 3x2 = ((-2 + -4x) + x(1 + 2x)) -8 + 2x + 3x2 = (-2 + -4x + (1 * x + 2x * x)) -8 + 2x + 3x2 = (-2 + -4x + (1x + 2x2)) Combine like terms: -4x + 1x = -3x -8 + 2x + 3x2 = (-2 + -3x + 2x2) Solving -8 + 2x + 3x2 = -2 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -8 + 2 + 2x + 3x + 3x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Combine like terms: -8 + 2 = -6 -6 + 2x + 3x + 3x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Combine like terms: 2x + 3x = 5x -6 + 5x + 3x2 + -2x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -6 + 5x + 1x2 = -2 + -3x + 2x2 + 2 + 3x + -2x2 Reorder the terms: -6 + 5x + 1x2 = -2 + 2 + -3x + 3x + 2x2 + -2x2 Combine like terms: -2 + 2 = 0 -6 + 5x + 1x2 = 0 + -3x + 3x + 2x2 + -2x2 -6 + 5x + 1x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -6 + 5x + 1x2 = 0 + 2x2 + -2x2 -6 + 5x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 5x + 1x2 = 0 Factor a trinomial. (-6 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 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 = 1Solution
x = {-6, 1}
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