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Simplifying (6x + 3)(6x + 3) = 0 Reorder the terms: (3 + 6x)(6x + 3) = 0 Reorder the terms: (3 + 6x)(3 + 6x) = 0 Multiply (3 + 6x) * (3 + 6x) (3(3 + 6x) + 6x * (3 + 6x)) = 0 ((3 * 3 + 6x * 3) + 6x * (3 + 6x)) = 0 ((9 + 18x) + 6x * (3 + 6x)) = 0 (9 + 18x + (3 * 6x + 6x * 6x)) = 0 (9 + 18x + (18x + 36x2)) = 0 Combine like terms: 18x + 18x = 36x (9 + 36x + 36x2) = 0 Solving 9 + 36x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(1 + 4x + 4x2) = 0 Factor a trinomial. 9((1 + 2x)(1 + 2x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-0.5, -0.5}
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