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Simplifying (4x + 8)(4x + -1) = 0 Reorder the terms: (8 + 4x)(4x + -1) = 0 Reorder the terms: (8 + 4x)(-1 + 4x) = 0 Multiply (8 + 4x) * (-1 + 4x) (8(-1 + 4x) + 4x * (-1 + 4x)) = 0 ((-1 * 8 + 4x * 8) + 4x * (-1 + 4x)) = 0 ((-8 + 32x) + 4x * (-1 + 4x)) = 0 (-8 + 32x + (-1 * 4x + 4x * 4x)) = 0 (-8 + 32x + (-4x + 16x2)) = 0 Combine like terms: 32x + -4x = 28x (-8 + 28x + 16x2) = 0 Solving -8 + 28x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 7x + 4x2) = 0 Factor a trinomial. 4((-2 + -1x)(1 + -4x)) = 0 Ignore the factor 4.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 '(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 = {-2, 0.25}
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