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Simplifying (3x + -2)(x + 9) = (x + -6)(1 + -3x) Reorder the terms: (-2 + 3x)(x + 9) = (x + -6)(1 + -3x) Reorder the terms: (-2 + 3x)(9 + x) = (x + -6)(1 + -3x) Multiply (-2 + 3x) * (9 + x) (-2(9 + x) + 3x * (9 + x)) = (x + -6)(1 + -3x) ((9 * -2 + x * -2) + 3x * (9 + x)) = (x + -6)(1 + -3x) ((-18 + -2x) + 3x * (9 + x)) = (x + -6)(1 + -3x) (-18 + -2x + (9 * 3x + x * 3x)) = (x + -6)(1 + -3x) (-18 + -2x + (27x + 3x2)) = (x + -6)(1 + -3x) Combine like terms: -2x + 27x = 25x (-18 + 25x + 3x2) = (x + -6)(1 + -3x) Reorder the terms: -18 + 25x + 3x2 = (-6 + x)(1 + -3x) Multiply (-6 + x) * (1 + -3x) -18 + 25x + 3x2 = (-6(1 + -3x) + x(1 + -3x)) -18 + 25x + 3x2 = ((1 * -6 + -3x * -6) + x(1 + -3x)) -18 + 25x + 3x2 = ((-6 + 18x) + x(1 + -3x)) -18 + 25x + 3x2 = (-6 + 18x + (1 * x + -3x * x)) -18 + 25x + 3x2 = (-6 + 18x + (1x + -3x2)) Combine like terms: 18x + 1x = 19x -18 + 25x + 3x2 = (-6 + 19x + -3x2) Solving -18 + 25x + 3x2 = -6 + 19x + -3x2 Solving for variable 'x'. Reorder the terms: -18 + 6 + 25x + -19x + 3x2 + 3x2 = -6 + 19x + -3x2 + 6 + -19x + 3x2 Combine like terms: -18 + 6 = -12 -12 + 25x + -19x + 3x2 + 3x2 = -6 + 19x + -3x2 + 6 + -19x + 3x2 Combine like terms: 25x + -19x = 6x -12 + 6x + 3x2 + 3x2 = -6 + 19x + -3x2 + 6 + -19x + 3x2 Combine like terms: 3x2 + 3x2 = 6x2 -12 + 6x + 6x2 = -6 + 19x + -3x2 + 6 + -19x + 3x2 Reorder the terms: -12 + 6x + 6x2 = -6 + 6 + 19x + -19x + -3x2 + 3x2 Combine like terms: -6 + 6 = 0 -12 + 6x + 6x2 = 0 + 19x + -19x + -3x2 + 3x2 -12 + 6x + 6x2 = 19x + -19x + -3x2 + 3x2 Combine like terms: 19x + -19x = 0 -12 + 6x + 6x2 = 0 + -3x2 + 3x2 -12 + 6x + 6x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -12 + 6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-2 + x + x2) = 0 Factor a trinomial. 6((-2 + -1x)(1 + -1x)) = 0 Ignore the factor 6.Subproblem 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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