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Simplifying (8x + -5)(6x + 3) = 0 Reorder the terms: (-5 + 8x)(6x + 3) = 0 Reorder the terms: (-5 + 8x)(3 + 6x) = 0 Multiply (-5 + 8x) * (3 + 6x) (-5(3 + 6x) + 8x * (3 + 6x)) = 0 ((3 * -5 + 6x * -5) + 8x * (3 + 6x)) = 0 ((-15 + -30x) + 8x * (3 + 6x)) = 0 (-15 + -30x + (3 * 8x + 6x * 8x)) = 0 (-15 + -30x + (24x + 48x2)) = 0 Combine like terms: -30x + 24x = -6x (-15 + -6x + 48x2) = 0 Solving -15 + -6x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -2x + 16x2) = 0 Factor a trinomial. 3((-1 + -2x)(5 + -8x)) = 0 Ignore the factor 3.Subproblem 1
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 = -0.5Subproblem 2
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 = 0.625Solution
x = {-0.5, 0.625}
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