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Simplifying (4x + 1)(3x + 6) = 0 Reorder the terms: (1 + 4x)(3x + 6) = 0 Reorder the terms: (1 + 4x)(6 + 3x) = 0 Multiply (1 + 4x) * (6 + 3x) (1(6 + 3x) + 4x * (6 + 3x)) = 0 ((6 * 1 + 3x * 1) + 4x * (6 + 3x)) = 0 ((6 + 3x) + 4x * (6 + 3x)) = 0 (6 + 3x + (6 * 4x + 3x * 4x)) = 0 (6 + 3x + (24x + 12x2)) = 0 Combine like terms: 3x + 24x = 27x (6 + 27x + 12x2) = 0 Solving 6 + 27x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 9x + 4x2) = 0 Factor a trinomial. 3((2 + x)(1 + 4x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 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 = {-2, -0.25}
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