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Simplifying x(x + 9)(2x + 3) = 0 Reorder the terms: x(9 + x)(2x + 3) = 0 Reorder the terms: x(9 + x)(3 + 2x) = 0 Multiply (9 + x) * (3 + 2x) x(9(3 + 2x) + x(3 + 2x)) = 0 x((3 * 9 + 2x * 9) + x(3 + 2x)) = 0 x((27 + 18x) + x(3 + 2x)) = 0 x(27 + 18x + (3 * x + 2x * x)) = 0 x(27 + 18x + (3x + 2x2)) = 0 Combine like terms: 18x + 3x = 21x x(27 + 21x + 2x2) = 0 (27 * x + 21x * x + 2x2 * x) = 0 (27x + 21x2 + 2x3) = 0 Solving 27x + 21x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(27 + 21x + 2x2) = 0 Factor a trinomial. x((9 + x)(3 + 2x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 3
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, -9, -1.5}
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