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Simplifying (x2 + 3x)(3x + 6) = 0 Reorder the terms: (3x + x2)(3x + 6) = 0 Reorder the terms: (3x + x2)(6 + 3x) = 0 Multiply (3x + x2) * (6 + 3x) (3x * (6 + 3x) + x2(6 + 3x)) = 0 ((6 * 3x + 3x * 3x) + x2(6 + 3x)) = 0 ((18x + 9x2) + x2(6 + 3x)) = 0 (18x + 9x2 + (6 * x2 + 3x * x2)) = 0 (18x + 9x2 + (6x2 + 3x3)) = 0 Combine like terms: 9x2 + 6x2 = 15x2 (18x + 15x2 + 3x3) = 0 Solving 18x + 15x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(6 + 5x + x2) = 0 Factor a trinomial. 3x((3 + x)(2 + x)) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {0, -3, -2}
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