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Simplifying (x + 3)(2x + -4) = (x + -2)(3x + 1) Reorder the terms: (3 + x)(2x + -4) = (x + -2)(3x + 1) Reorder the terms: (3 + x)(-4 + 2x) = (x + -2)(3x + 1) Multiply (3 + x) * (-4 + 2x) (3(-4 + 2x) + x(-4 + 2x)) = (x + -2)(3x + 1) ((-4 * 3 + 2x * 3) + x(-4 + 2x)) = (x + -2)(3x + 1) ((-12 + 6x) + x(-4 + 2x)) = (x + -2)(3x + 1) (-12 + 6x + (-4 * x + 2x * x)) = (x + -2)(3x + 1) (-12 + 6x + (-4x + 2x2)) = (x + -2)(3x + 1) Combine like terms: 6x + -4x = 2x (-12 + 2x + 2x2) = (x + -2)(3x + 1) Reorder the terms: -12 + 2x + 2x2 = (-2 + x)(3x + 1) Reorder the terms: -12 + 2x + 2x2 = (-2 + x)(1 + 3x) Multiply (-2 + x) * (1 + 3x) -12 + 2x + 2x2 = (-2(1 + 3x) + x(1 + 3x)) -12 + 2x + 2x2 = ((1 * -2 + 3x * -2) + x(1 + 3x)) -12 + 2x + 2x2 = ((-2 + -6x) + x(1 + 3x)) -12 + 2x + 2x2 = (-2 + -6x + (1 * x + 3x * x)) -12 + 2x + 2x2 = (-2 + -6x + (1x + 3x2)) Combine like terms: -6x + 1x = -5x -12 + 2x + 2x2 = (-2 + -5x + 3x2) Solving -12 + 2x + 2x2 = -2 + -5x + 3x2 Solving for variable 'x'. Reorder the terms: -12 + 2 + 2x + 5x + 2x2 + -3x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2 Combine like terms: -12 + 2 = -10 -10 + 2x + 5x + 2x2 + -3x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2 Combine like terms: 2x + 5x = 7x -10 + 7x + 2x2 + -3x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 -10 + 7x + -1x2 = -2 + -5x + 3x2 + 2 + 5x + -3x2 Reorder the terms: -10 + 7x + -1x2 = -2 + 2 + -5x + 5x + 3x2 + -3x2 Combine like terms: -2 + 2 = 0 -10 + 7x + -1x2 = 0 + -5x + 5x + 3x2 + -3x2 -10 + 7x + -1x2 = -5x + 5x + 3x2 + -3x2 Combine like terms: -5x + 5x = 0 -10 + 7x + -1x2 = 0 + 3x2 + -3x2 -10 + 7x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -10 + 7x + -1x2 = 0 Factor a trinomial. (-5 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
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 = {5, 2}
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