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Simplifying (6x + 6)(8x + 6) + 18x + 18 = 0 Reorder the terms: (6 + 6x)(8x + 6) + 18x + 18 = 0 Reorder the terms: (6 + 6x)(6 + 8x) + 18x + 18 = 0 Multiply (6 + 6x) * (6 + 8x) (6(6 + 8x) + 6x * (6 + 8x)) + 18x + 18 = 0 ((6 * 6 + 8x * 6) + 6x * (6 + 8x)) + 18x + 18 = 0 ((36 + 48x) + 6x * (6 + 8x)) + 18x + 18 = 0 (36 + 48x + (6 * 6x + 8x * 6x)) + 18x + 18 = 0 (36 + 48x + (36x + 48x2)) + 18x + 18 = 0 Combine like terms: 48x + 36x = 84x (36 + 84x + 48x2) + 18x + 18 = 0 Reorder the terms: 36 + 18 + 84x + 18x + 48x2 = 0 Combine like terms: 36 + 18 = 54 54 + 84x + 18x + 48x2 = 0 Combine like terms: 84x + 18x = 102x 54 + 102x + 48x2 = 0 Solving 54 + 102x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(9 + 17x + 8x2) = 0 Factor a trinomial. 6((9 + 8x)(1 + x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(9 + 8x)' equal to zero and attempt to solve: Simplifying 9 + 8x = 0 Solving 9 + 8x = 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 + 8x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x = 0 + -9 8x = 0 + -9 Combine like terms: 0 + -9 = -9 8x = -9 Divide each side by '8'. x = -1.125 Simplifying x = -1.125Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-1.125, -1}
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