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Simplifying x(2x + 1)(3x + 9) = 0 Reorder the terms: x(1 + 2x)(3x + 9) = 0 Reorder the terms: x(1 + 2x)(9 + 3x) = 0 Multiply (1 + 2x) * (9 + 3x) x(1(9 + 3x) + 2x * (9 + 3x)) = 0 x((9 * 1 + 3x * 1) + 2x * (9 + 3x)) = 0 x((9 + 3x) + 2x * (9 + 3x)) = 0 x(9 + 3x + (9 * 2x + 3x * 2x)) = 0 x(9 + 3x + (18x + 6x2)) = 0 Combine like terms: 3x + 18x = 21x x(9 + 21x + 6x2) = 0 (9 * x + 21x * x + 6x2 * x) = 0 (9x + 21x2 + 6x3) = 0 Solving 9x + 21x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(3 + 7x + 2x2) = 0 Factor a trinomial. 3x((3 + x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 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 '(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 = -3Subproblem 3
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {0, -3, -0.5}
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