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