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Simplifying 3(2x + 1)(4x + 3) = 0 Reorder the terms: 3(1 + 2x)(4x + 3) = 0 Reorder the terms: 3(1 + 2x)(3 + 4x) = 0 Multiply (1 + 2x) * (3 + 4x) 3(1(3 + 4x) + 2x * (3 + 4x)) = 0 3((3 * 1 + 4x * 1) + 2x * (3 + 4x)) = 0 3((3 + 4x) + 2x * (3 + 4x)) = 0 3(3 + 4x + (3 * 2x + 4x * 2x)) = 0 3(3 + 4x + (6x + 8x2)) = 0 Combine like terms: 4x + 6x = 10x 3(3 + 10x + 8x2) = 0 (3 * 3 + 10x * 3 + 8x2 * 3) = 0 (9 + 30x + 24x2) = 0 Solving 9 + 30x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 10x + 8x2) = 0 Factor a trinomial. 3((3 + 4x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Subproblem 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 = {-0.75, -0.5}
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