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Simplifying (x + 3)(3x + -4) = (x + 4)(2x + -1) Reorder the terms: (3 + x)(3x + -4) = (x + 4)(2x + -1) Reorder the terms: (3 + x)(-4 + 3x) = (x + 4)(2x + -1) Multiply (3 + x) * (-4 + 3x) (3(-4 + 3x) + x(-4 + 3x)) = (x + 4)(2x + -1) ((-4 * 3 + 3x * 3) + x(-4 + 3x)) = (x + 4)(2x + -1) ((-12 + 9x) + x(-4 + 3x)) = (x + 4)(2x + -1) (-12 + 9x + (-4 * x + 3x * x)) = (x + 4)(2x + -1) (-12 + 9x + (-4x + 3x2)) = (x + 4)(2x + -1) Combine like terms: 9x + -4x = 5x (-12 + 5x + 3x2) = (x + 4)(2x + -1) Reorder the terms: -12 + 5x + 3x2 = (4 + x)(2x + -1) Reorder the terms: -12 + 5x + 3x2 = (4 + x)(-1 + 2x) Multiply (4 + x) * (-1 + 2x) -12 + 5x + 3x2 = (4(-1 + 2x) + x(-1 + 2x)) -12 + 5x + 3x2 = ((-1 * 4 + 2x * 4) + x(-1 + 2x)) -12 + 5x + 3x2 = ((-4 + 8x) + x(-1 + 2x)) -12 + 5x + 3x2 = (-4 + 8x + (-1 * x + 2x * x)) -12 + 5x + 3x2 = (-4 + 8x + (-1x + 2x2)) Combine like terms: 8x + -1x = 7x -12 + 5x + 3x2 = (-4 + 7x + 2x2) Solving -12 + 5x + 3x2 = -4 + 7x + 2x2 Solving for variable 'x'. Reorder the terms: -12 + 4 + 5x + -7x + 3x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Combine like terms: -12 + 4 = -8 -8 + 5x + -7x + 3x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Combine like terms: 5x + -7x = -2x -8 + -2x + 3x2 + -2x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -8 + -2x + 1x2 = -4 + 7x + 2x2 + 4 + -7x + -2x2 Reorder the terms: -8 + -2x + 1x2 = -4 + 4 + 7x + -7x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 -8 + -2x + 1x2 = 0 + 7x + -7x + 2x2 + -2x2 -8 + -2x + 1x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -8 + -2x + 1x2 = 0 + 2x2 + -2x2 -8 + -2x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + -2x + 1x2 = 0 Factor a trinomial. (-2 + -1x)(4 + -1x) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-2, 4}
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