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Simplifying (3 + -12x)(2x + 9) = 0 Reorder the terms: (3 + -12x)(9 + 2x) = 0 Multiply (3 + -12x) * (9 + 2x) (3(9 + 2x) + -12x * (9 + 2x)) = 0 ((9 * 3 + 2x * 3) + -12x * (9 + 2x)) = 0 ((27 + 6x) + -12x * (9 + 2x)) = 0 (27 + 6x + (9 * -12x + 2x * -12x)) = 0 (27 + 6x + (-108x + -24x2)) = 0 Combine like terms: 6x + -108x = -102x (27 + -102x + -24x2) = 0 Solving 27 + -102x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -34x + -8x2) = 0 Factor a trinomial. 3((1 + -4x)(9 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
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 = -4.5Solution
x = {0.25, -4.5}
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