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Simplifying 2x(3 + -1x)(2x + 1) = 0 Reorder the terms: 2x(3 + -1x)(1 + 2x) = 0 Multiply (3 + -1x) * (1 + 2x) 2x(3(1 + 2x) + -1x * (1 + 2x)) = 0 2x((1 * 3 + 2x * 3) + -1x * (1 + 2x)) = 0 2x((3 + 6x) + -1x * (1 + 2x)) = 0 2x(3 + 6x + (1 * -1x + 2x * -1x)) = 0 2x(3 + 6x + (-1x + -2x2)) = 0 Combine like terms: 6x + -1x = 5x 2x(3 + 5x + -2x2) = 0 (3 * 2x + 5x * 2x + -2x2 * 2x) = 0 (6x + 10x2 + -4x3) = 0 Solving 6x + 10x2 + -4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + 5x + -2x2) = 0 Factor a trinomial. 2x((3 + -1x)(1 + 2x)) = 0 Ignore the factor 2.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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. 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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