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Simplifying (6x + 1)(9x + 27) = 0 Reorder the terms: (1 + 6x)(9x + 27) = 0 Reorder the terms: (1 + 6x)(27 + 9x) = 0 Multiply (1 + 6x) * (27 + 9x) (1(27 + 9x) + 6x * (27 + 9x)) = 0 ((27 * 1 + 9x * 1) + 6x * (27 + 9x)) = 0 ((27 + 9x) + 6x * (27 + 9x)) = 0 (27 + 9x + (27 * 6x + 9x * 6x)) = 0 (27 + 9x + (162x + 54x2)) = 0 Combine like terms: 9x + 162x = 171x (27 + 171x + 54x2) = 0 Solving 27 + 171x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 19x + 6x2) = 0 Factor a trinomial. 9((3 + x)(1 + 6x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + 6x)' equal to zero and attempt to solve: Simplifying 1 + 6x = 0 Solving 1 + 6x = 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 + 6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x = 0 + -1 6x = 0 + -1 Combine like terms: 0 + -1 = -1 6x = -1 Divide each side by '6'. x = -0.1666666667 Simplifying x = -0.1666666667Solution
x = {-3, -0.1666666667}
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