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Simplifying (4x + 1)(6x + 3) = 0 Reorder the terms: (1 + 4x)(6x + 3) = 0 Reorder the terms: (1 + 4x)(3 + 6x) = 0 Multiply (1 + 4x) * (3 + 6x) (1(3 + 6x) + 4x * (3 + 6x)) = 0 ((3 * 1 + 6x * 1) + 4x * (3 + 6x)) = 0 ((3 + 6x) + 4x * (3 + 6x)) = 0 (3 + 6x + (3 * 4x + 6x * 4x)) = 0 (3 + 6x + (12x + 24x2)) = 0 Combine like terms: 6x + 12x = 18x (3 + 18x + 24x2) = 0 Solving 3 + 18x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + 6x + 8x2) = 0 Factor a trinomial. 3((1 + 2x)(1 + 4x)) = 0 Ignore the factor 3.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 + 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 = -0.25Solution
x = {-0.5, -0.25}
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