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Simplifying (9 + -2x)(9 + 3x) = 0 Multiply (9 + -2x) * (9 + 3x) (9(9 + 3x) + -2x * (9 + 3x)) = 0 ((9 * 9 + 3x * 9) + -2x * (9 + 3x)) = 0 ((81 + 27x) + -2x * (9 + 3x)) = 0 (81 + 27x + (9 * -2x + 3x * -2x)) = 0 (81 + 27x + (-18x + -6x2)) = 0 Combine like terms: 27x + -18x = 9x (81 + 9x + -6x2) = 0 Solving 81 + 9x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(27 + 3x + -2x2) = 0 Factor a trinomial. 3((9 + -2x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {4.5, -3}
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