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Simplifying 2x(x + 1)(3x + -1) = 0 Reorder the terms: 2x(1 + x)(3x + -1) = 0 Reorder the terms: 2x(1 + x)(-1 + 3x) = 0 Multiply (1 + x) * (-1 + 3x) 2x(1(-1 + 3x) + x(-1 + 3x)) = 0 2x((-1 * 1 + 3x * 1) + x(-1 + 3x)) = 0 2x((-1 + 3x) + x(-1 + 3x)) = 0 2x(-1 + 3x + (-1 * x + 3x * x)) = 0 2x(-1 + 3x + (-1x + 3x2)) = 0 Combine like terms: 3x + -1x = 2x 2x(-1 + 2x + 3x2) = 0 (-1 * 2x + 2x * 2x + 3x2 * 2x) = 0 (-2x + 4x2 + 6x3) = 0 Solving -2x + 4x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-1 + 2x + 3x2) = 0 Factor a trinomial. 2x((-1 + -1x)(1 + -3x)) = 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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 3
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {0, -1, 0.3333333333}
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