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Simplifying (2x + 3) * x(-1x + -2) = 0 Reorder the terms: (3 + 2x) * x(-1x + -2) = 0 Reorder the terms: (3 + 2x) * x(-2 + -1x) = 0 Reorder the terms for easier multiplication: x(3 + 2x)(-2 + -1x) = 0 Multiply (3 + 2x) * (-2 + -1x) x(3(-2 + -1x) + 2x * (-2 + -1x)) = 0 x((-2 * 3 + -1x * 3) + 2x * (-2 + -1x)) = 0 x((-6 + -3x) + 2x * (-2 + -1x)) = 0 x(-6 + -3x + (-2 * 2x + -1x * 2x)) = 0 x(-6 + -3x + (-4x + -2x2)) = 0 Combine like terms: -3x + -4x = -7x x(-6 + -7x + -2x2) = 0 (-6 * x + -7x * x + -2x2 * x) = 0 (-6x + -7x2 + -2x3) = 0 Solving -6x + -7x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(6 + 7x + 2x2) = 0 Factor a trinomial. -1x((2 + x)(3 + 2x)) = 0 Ignore the factor -1.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 '(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 = -2Subproblem 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, -2, -1.5}
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