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Simplifying (3x + 6)(2x + -4) = (5x + -11)(x + 2) Reorder the terms: (6 + 3x)(2x + -4) = (5x + -11)(x + 2) Reorder the terms: (6 + 3x)(-4 + 2x) = (5x + -11)(x + 2) Multiply (6 + 3x) * (-4 + 2x) (6(-4 + 2x) + 3x * (-4 + 2x)) = (5x + -11)(x + 2) ((-4 * 6 + 2x * 6) + 3x * (-4 + 2x)) = (5x + -11)(x + 2) ((-24 + 12x) + 3x * (-4 + 2x)) = (5x + -11)(x + 2) (-24 + 12x + (-4 * 3x + 2x * 3x)) = (5x + -11)(x + 2) (-24 + 12x + (-12x + 6x2)) = (5x + -11)(x + 2) Combine like terms: 12x + -12x = 0 (-24 + 0 + 6x2) = (5x + -11)(x + 2) (-24 + 6x2) = (5x + -11)(x + 2) Reorder the terms: -24 + 6x2 = (-11 + 5x)(x + 2) Reorder the terms: -24 + 6x2 = (-11 + 5x)(2 + x) Multiply (-11 + 5x) * (2 + x) -24 + 6x2 = (-11(2 + x) + 5x * (2 + x)) -24 + 6x2 = ((2 * -11 + x * -11) + 5x * (2 + x)) -24 + 6x2 = ((-22 + -11x) + 5x * (2 + x)) -24 + 6x2 = (-22 + -11x + (2 * 5x + x * 5x)) -24 + 6x2 = (-22 + -11x + (10x + 5x2)) Combine like terms: -11x + 10x = -1x -24 + 6x2 = (-22 + -1x + 5x2) Solving -24 + 6x2 = -22 + -1x + 5x2 Solving for variable 'x'. Reorder the terms: -24 + 22 + x + 6x2 + -5x2 = -22 + -1x + 5x2 + 22 + x + -5x2 Combine like terms: -24 + 22 = -2 -2 + x + 6x2 + -5x2 = -22 + -1x + 5x2 + 22 + x + -5x2 Combine like terms: 6x2 + -5x2 = 1x2 -2 + x + 1x2 = -22 + -1x + 5x2 + 22 + x + -5x2 Reorder the terms: -2 + x + 1x2 = -22 + 22 + -1x + x + 5x2 + -5x2 Combine like terms: -22 + 22 = 0 -2 + x + 1x2 = 0 + -1x + x + 5x2 + -5x2 -2 + x + 1x2 = -1x + x + 5x2 + -5x2 Combine like terms: -1x + x = 0 -2 + x + 1x2 = 0 + 5x2 + -5x2 -2 + x + 1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -2 + x + 1x2 = 0 Factor a trinomial. (-2 + -1x)(1 + -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 '(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 = {-2, 1}
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