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Simplifying (8x + 6)(8x + 4) = 0 Reorder the terms: (6 + 8x)(8x + 4) = 0 Reorder the terms: (6 + 8x)(4 + 8x) = 0 Multiply (6 + 8x) * (4 + 8x) (6(4 + 8x) + 8x * (4 + 8x)) = 0 ((4 * 6 + 8x * 6) + 8x * (4 + 8x)) = 0 ((24 + 48x) + 8x * (4 + 8x)) = 0 (24 + 48x + (4 * 8x + 8x * 8x)) = 0 (24 + 48x + (32x + 64x2)) = 0 Combine like terms: 48x + 32x = 80x (24 + 80x + 64x2) = 0 Solving 24 + 80x + 64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(3 + 10x + 8x2) = 0 Factor a trinomial. 8((3 + 4x)(1 + 2x)) = 0 Ignore the factor 8.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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