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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 = -1x x(-3 + -1x + 2x2) = 0 (-3 * x + -1x * x + 2x2 * x) = 0 (-3x + -1x2 + 2x3) = 0 Solving -3x + -1x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + -1x + 2x2) = 0 Factor a trinomial. x((-1 + -1x)(3 + -2x)) = 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 '(-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 '(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 = 1.5Solution
x = {0, -1, 1.5}
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