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Simplifying 8(x + -6)(4x + 5) = 0 Reorder the terms: 8(-6 + x)(4x + 5) = 0 Reorder the terms: 8(-6 + x)(5 + 4x) = 0 Multiply (-6 + x) * (5 + 4x) 8(-6(5 + 4x) + x(5 + 4x)) = 0 8((5 * -6 + 4x * -6) + x(5 + 4x)) = 0 8((-30 + -24x) + x(5 + 4x)) = 0 8(-30 + -24x + (5 * x + 4x * x)) = 0 8(-30 + -24x + (5x + 4x2)) = 0 Combine like terms: -24x + 5x = -19x 8(-30 + -19x + 4x2) = 0 (-30 * 8 + -19x * 8 + 4x2 * 8) = 0 (-240 + -152x + 32x2) = 0 Solving -240 + -152x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-30 + -19x + 4x2) = 0 Factor a trinomial. 8((-5 + -4x)(6 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-1.25, 6}
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