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Simplifying (12x + 3)(6x + 1) = 0 Reorder the terms: (3 + 12x)(6x + 1) = 0 Reorder the terms: (3 + 12x)(1 + 6x) = 0 Multiply (3 + 12x) * (1 + 6x) (3(1 + 6x) + 12x * (1 + 6x)) = 0 ((1 * 3 + 6x * 3) + 12x * (1 + 6x)) = 0 ((3 + 18x) + 12x * (1 + 6x)) = 0 (3 + 18x + (1 * 12x + 6x * 12x)) = 0 (3 + 18x + (12x + 72x2)) = 0 Combine like terms: 18x + 12x = 30x (3 + 30x + 72x2) = 0 Solving 3 + 30x + 72x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 10x + 24x2) = 0 Factor a trinomial. 3((1 + 4x)(1 + 6x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Subproblem 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 = {-0.25, -0.1666666667}
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