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