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Simplifying 8(4x + -1)(x + 4) = 0 Reorder the terms: 8(-1 + 4x)(x + 4) = 0 Reorder the terms: 8(-1 + 4x)(4 + x) = 0 Multiply (-1 + 4x) * (4 + x) 8(-1(4 + x) + 4x * (4 + x)) = 0 8((4 * -1 + x * -1) + 4x * (4 + x)) = 0 8((-4 + -1x) + 4x * (4 + x)) = 0 8(-4 + -1x + (4 * 4x + x * 4x)) = 0 8(-4 + -1x + (16x + 4x2)) = 0 Combine like terms: -1x + 16x = 15x 8(-4 + 15x + 4x2) = 0 (-4 * 8 + 15x * 8 + 4x2 * 8) = 0 (-32 + 120x + 32x2) = 0 Solving -32 + 120x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + 15x + 4x2) = 0 Factor a trinomial. 8((-4 + -1x)(1 + -4x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-4, 0.25}
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