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Simplifying (6x + 3)(8x + 5) = 0 Reorder the terms: (3 + 6x)(8x + 5) = 0 Reorder the terms: (3 + 6x)(5 + 8x) = 0 Multiply (3 + 6x) * (5 + 8x) (3(5 + 8x) + 6x * (5 + 8x)) = 0 ((5 * 3 + 8x * 3) + 6x * (5 + 8x)) = 0 ((15 + 24x) + 6x * (5 + 8x)) = 0 (15 + 24x + (5 * 6x + 8x * 6x)) = 0 (15 + 24x + (30x + 48x2)) = 0 Combine like terms: 24x + 30x = 54x (15 + 54x + 48x2) = 0 Solving 15 + 54x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 18x + 16x2) = 0 Factor a trinomial. 3((5 + 8x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + 8x)' equal to zero and attempt to solve: Simplifying 5 + 8x = 0 Solving 5 + 8x = 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 + 8x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8x = 0 + -5 8x = 0 + -5 Combine like terms: 0 + -5 = -5 8x = -5 Divide each side by '8'. x = -0.625 Simplifying x = -0.625Subproblem 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 = {-0.625, -0.5}
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