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Simplifying (x + -6)(9x + 2) = -25(x + -6) Reorder the terms: (-6 + x)(9x + 2) = -25(x + -6) Reorder the terms: (-6 + x)(2 + 9x) = -25(x + -6) Multiply (-6 + x) * (2 + 9x) (-6(2 + 9x) + x(2 + 9x)) = -25(x + -6) ((2 * -6 + 9x * -6) + x(2 + 9x)) = -25(x + -6) ((-12 + -54x) + x(2 + 9x)) = -25(x + -6) (-12 + -54x + (2 * x + 9x * x)) = -25(x + -6) (-12 + -54x + (2x + 9x2)) = -25(x + -6) Combine like terms: -54x + 2x = -52x (-12 + -52x + 9x2) = -25(x + -6) Reorder the terms: -12 + -52x + 9x2 = -25(-6 + x) -12 + -52x + 9x2 = (-6 * -25 + x * -25) -12 + -52x + 9x2 = (150 + -25x) Solving -12 + -52x + 9x2 = 150 + -25x Solving for variable 'x'. Reorder the terms: -12 + -150 + -52x + 25x + 9x2 = 150 + -25x + -150 + 25x Combine like terms: -12 + -150 = -162 -162 + -52x + 25x + 9x2 = 150 + -25x + -150 + 25x Combine like terms: -52x + 25x = -27x -162 + -27x + 9x2 = 150 + -25x + -150 + 25x Reorder the terms: -162 + -27x + 9x2 = 150 + -150 + -25x + 25x Combine like terms: 150 + -150 = 0 -162 + -27x + 9x2 = 0 + -25x + 25x -162 + -27x + 9x2 = -25x + 25x Combine like terms: -25x + 25x = 0 -162 + -27x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-18 + -3x + x2) = 0 Factor a trinomial. 9((-3 + -1x)(6 + -1x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
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 = 6Solution
x = {-3, 6}
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