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Simplifying (8x + -5)(3x + 6) = 0 Reorder the terms: (-5 + 8x)(3x + 6) = 0 Reorder the terms: (-5 + 8x)(6 + 3x) = 0 Multiply (-5 + 8x) * (6 + 3x) (-5(6 + 3x) + 8x * (6 + 3x)) = 0 ((6 * -5 + 3x * -5) + 8x * (6 + 3x)) = 0 ((-30 + -15x) + 8x * (6 + 3x)) = 0 (-30 + -15x + (6 * 8x + 3x * 8x)) = 0 (-30 + -15x + (48x + 24x2)) = 0 Combine like terms: -15x + 48x = 33x (-30 + 33x + 24x2) = 0 Solving -30 + 33x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 11x + 8x2) = 0 Factor a trinomial. 3((-2 + -1x)(5 + -8x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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 = {-2, 0.625}
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