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Simplifying (-4 + x)(4x + -4) = 0 Reorder the terms: (-4 + x)(-4 + 4x) = 0 Multiply (-4 + x) * (-4 + 4x) (-4(-4 + 4x) + x(-4 + 4x)) = 0 ((-4 * -4 + 4x * -4) + x(-4 + 4x)) = 0 ((16 + -16x) + x(-4 + 4x)) = 0 (16 + -16x + (-4 * x + 4x * x)) = 0 (16 + -16x + (-4x + 4x2)) = 0 Combine like terms: -16x + -4x = -20x (16 + -20x + 4x2) = 0 Solving 16 + -20x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -5x + x2) = 0 Factor a trinomial. 4((1 + -1x)(4 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
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 = 4Solution
x = {1, 4}
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