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Simplifying (4x + 6)(8x + 2) = 0 Reorder the terms: (6 + 4x)(8x + 2) = 0 Reorder the terms: (6 + 4x)(2 + 8x) = 0 Multiply (6 + 4x) * (2 + 8x) (6(2 + 8x) + 4x * (2 + 8x)) = 0 ((2 * 6 + 8x * 6) + 4x * (2 + 8x)) = 0 ((12 + 48x) + 4x * (2 + 8x)) = 0 (12 + 48x + (2 * 4x + 8x * 4x)) = 0 (12 + 48x + (8x + 32x2)) = 0 Combine like terms: 48x + 8x = 56x (12 + 56x + 32x2) = 0 Solving 12 + 56x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + 14x + 8x2) = 0 Factor a trinomial. 4((3 + 2x)(1 + 4x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 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 = {-1.5, -0.25}
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