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Simplifying (9x + 6)(6x + -9) = 0 Reorder the terms: (6 + 9x)(6x + -9) = 0 Reorder the terms: (6 + 9x)(-9 + 6x) = 0 Multiply (6 + 9x) * (-9 + 6x) (6(-9 + 6x) + 9x * (-9 + 6x)) = 0 ((-9 * 6 + 6x * 6) + 9x * (-9 + 6x)) = 0 ((-54 + 36x) + 9x * (-9 + 6x)) = 0 (-54 + 36x + (-9 * 9x + 6x * 9x)) = 0 (-54 + 36x + (-81x + 54x2)) = 0 Combine like terms: 36x + -81x = -45x (-54 + -45x + 54x2) = 0 Solving -54 + -45x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(-6 + -5x + 6x2) = 0 Factor a trinomial. 9((-2 + -3x)(3 + -2x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve: Simplifying -2 + -3x = 0 Solving -2 + -3x = 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 + -3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3x = 0 + 2 -3x = 0 + 2 Combine like terms: 0 + 2 = 2 -3x = 2 Divide each side by '-3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-0.6666666667, 1.5}
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