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Simplifying x(x + 1)(2x + 3) = 0 Reorder the terms: x(1 + x)(2x + 3) = 0 Reorder the terms: x(1 + x)(3 + 2x) = 0 Multiply (1 + x) * (3 + 2x) x(1(3 + 2x) + x(3 + 2x)) = 0 x((3 * 1 + 2x * 1) + x(3 + 2x)) = 0 x((3 + 2x) + x(3 + 2x)) = 0 x(3 + 2x + (3 * x + 2x * x)) = 0 x(3 + 2x + (3x + 2x2)) = 0 Combine like terms: 2x + 3x = 5x x(3 + 5x + 2x2) = 0 (3 * x + 5x * x + 2x2 * x) = 0 (3x + 5x2 + 2x3) = 0 Solving 3x + 5x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 5x + 2x2) = 0 Factor a trinomial. x((3 + 2x)(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {0, -1.5, -1}
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