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Simplifying 3(x2 + 3x) + -2x(x2 + 3x) = 0 Reorder the terms: 3(3x + x2) + -2x(x2 + 3x) = 0 (3x * 3 + x2 * 3) + -2x(x2 + 3x) = 0 (9x + 3x2) + -2x(x2 + 3x) = 0 Reorder the terms: 9x + 3x2 + -2x(3x + x2) = 0 9x + 3x2 + (3x * -2x + x2 * -2x) = 0 9x + 3x2 + (-6x2 + -2x3) = 0 Combine like terms: 3x2 + -6x2 = -3x2 9x + -3x2 + -2x3 = 0 Solving 9x + -3x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(9 + -3x + -2x2) = 0 Factor a trinomial. x((3 + -2x)(3 + x)) = 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 '(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 = 1.5Subproblem 3
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 = {0, 1.5, -3}
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