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Simplifying (x + -3)[(x + -3) + (2x + 9)] = 9[9 + (3x + 2)] Reorder the terms: (-3 + x)[(x + -3) + (2x + 9)] = 9[9 + (3x + 2)] Reorder the terms: (-3 + x)[(-3 + x) + (2x + 9)] = 9[9 + (3x + 2)] Remove parenthesis around (-3 + x) (-3 + x)[-3 + x + (2x + 9)] = 9[9 + (3x + 2)] Reorder the terms: (-3 + x)[-3 + x + (9 + 2x)] = 9[9 + (3x + 2)] Remove parenthesis around (9 + 2x) (-3 + x)[-3 + x + 9 + 2x] = 9[9 + (3x + 2)] Reorder the terms: (-3 + x)[-3 + 9 + x + 2x] = 9[9 + (3x + 2)] Combine like terms: -3 + 9 = 6 (-3 + x)[6 + x + 2x] = 9[9 + (3x + 2)] Combine like terms: x + 2x = 3x (-3 + x)[6 + 3x] = 9[9 + (3x + 2)] Multiply (-3 + x) * [6 + 3x] (-3[6 + 3x] + x[6 + 3x]) = 9[9 + (3x + 2)] ([6 * -3 + 3x * -3] + x[6 + 3x]) = 9[9 + (3x + 2)] ([-18 + -9x] + x[6 + 3x]) = 9[9 + (3x + 2)] (-18 + -9x + [6 * x + 3x * x]) = 9[9 + (3x + 2)] (-18 + -9x + [6x + 3x2]) = 9[9 + (3x + 2)] Combine like terms: -9x + 6x = -3x (-18 + -3x + 3x2) = 9[9 + (3x + 2)] Reorder the terms: -18 + -3x + 3x2 = 9[9 + (2 + 3x)] Remove parenthesis around (2 + 3x) -18 + -3x + 3x2 = 9[9 + 2 + 3x] Combine like terms: 9 + 2 = 11 -18 + -3x + 3x2 = 9[11 + 3x] -18 + -3x + 3x2 = [11 * 9 + 3x * 9] -18 + -3x + 3x2 = [99 + 27x] Solving -18 + -3x + 3x2 = 99 + 27x Solving for variable 'x'. Reorder the terms: -18 + -99 + -3x + -27x + 3x2 = 99 + 27x + -99 + -27x Combine like terms: -18 + -99 = -117 -117 + -3x + -27x + 3x2 = 99 + 27x + -99 + -27x Combine like terms: -3x + -27x = -30x -117 + -30x + 3x2 = 99 + 27x + -99 + -27x Reorder the terms: -117 + -30x + 3x2 = 99 + -99 + 27x + -27x Combine like terms: 99 + -99 = 0 -117 + -30x + 3x2 = 0 + 27x + -27x -117 + -30x + 3x2 = 27x + -27x Combine like terms: 27x + -27x = 0 -117 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-39 + -10x + x2) = 0 Factor a trinomial. 3((-3 + -1x)(13 + -1x)) = 0 Ignore the factor 3.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 '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-3, 13}
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