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Simplifying (2 + -1x)(6x + 9) = 0 Reorder the terms: (2 + -1x)(9 + 6x) = 0 Multiply (2 + -1x) * (9 + 6x) (2(9 + 6x) + -1x * (9 + 6x)) = 0 ((9 * 2 + 6x * 2) + -1x * (9 + 6x)) = 0 ((18 + 12x) + -1x * (9 + 6x)) = 0 (18 + 12x + (9 * -1x + 6x * -1x)) = 0 (18 + 12x + (-9x + -6x2)) = 0 Combine like terms: 12x + -9x = 3x (18 + 3x + -6x2) = 0 Solving 18 + 3x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + x + -2x2) = 0 Factor a trinomial. 3((2 + -1x)(3 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {2, -1.5}
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