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Simplifying (8x + 6)(2x + 5) = 0 Reorder the terms: (6 + 8x)(2x + 5) = 0 Reorder the terms: (6 + 8x)(5 + 2x) = 0 Multiply (6 + 8x) * (5 + 2x) (6(5 + 2x) + 8x * (5 + 2x)) = 0 ((5 * 6 + 2x * 6) + 8x * (5 + 2x)) = 0 ((30 + 12x) + 8x * (5 + 2x)) = 0 (30 + 12x + (5 * 8x + 2x * 8x)) = 0 (30 + 12x + (40x + 16x2)) = 0 Combine like terms: 12x + 40x = 52x (30 + 52x + 16x2) = 0 Solving 30 + 52x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 26x + 8x2) = 0 Factor a trinomial. 2((5 + 2x)(3 + 4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 2
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 = -0.75Solution
x = {-2.5, -0.75}
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