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Simplifying (2x + -3) * 2(2x + 9) = 0 Reorder the terms: (-3 + 2x) * 2(2x + 9) = 0 Reorder the terms: (-3 + 2x) * 2(9 + 2x) = 0 Reorder the terms for easier multiplication: 2(-3 + 2x)(9 + 2x) = 0 Multiply (-3 + 2x) * (9 + 2x) 2(-3(9 + 2x) + 2x * (9 + 2x)) = 0 2((9 * -3 + 2x * -3) + 2x * (9 + 2x)) = 0 2((-27 + -6x) + 2x * (9 + 2x)) = 0 2(-27 + -6x + (9 * 2x + 2x * 2x)) = 0 2(-27 + -6x + (18x + 4x2)) = 0 Combine like terms: -6x + 18x = 12x 2(-27 + 12x + 4x2) = 0 (-27 * 2 + 12x * 2 + 4x2 * 2) = 0 (-54 + 24x + 8x2) = 0 Solving -54 + 24x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 12x + 4x2) = 0 Factor a trinomial. 2((-9 + -2x)(3 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
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 = {-4.5, 1.5}
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