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Simplifying (6x + 27)(9x + 1) = 0 Reorder the terms: (27 + 6x)(9x + 1) = 0 Reorder the terms: (27 + 6x)(1 + 9x) = 0 Multiply (27 + 6x) * (1 + 9x) (27(1 + 9x) + 6x * (1 + 9x)) = 0 ((1 * 27 + 9x * 27) + 6x * (1 + 9x)) = 0 ((27 + 243x) + 6x * (1 + 9x)) = 0 (27 + 243x + (1 * 6x + 9x * 6x)) = 0 (27 + 243x + (6x + 54x2)) = 0 Combine like terms: 243x + 6x = 249x (27 + 249x + 54x2) = 0 Solving 27 + 249x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 83x + 18x2) = 0 Factor a trinomial. 3((9 + 2x)(1 + 9x)) = 0 Ignore the factor 3.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 '(1 + 9x)' equal to zero and attempt to solve: Simplifying 1 + 9x = 0 Solving 1 + 9x = 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 + 9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 9x = 0 + -1 9x = 0 + -1 Combine like terms: 0 + -1 = -1 9x = -1 Divide each side by '9'. x = -0.1111111111 Simplifying x = -0.1111111111Solution
x = {-4.5, -0.1111111111}
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