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Simplifying 0 = (4x + -4)(x2 + 5x)(x) Reorder the terms: 0 = (-4 + 4x)(x2 + 5x)(x) Reorder the terms: 0 = (-4 + 4x)(5x + x2)(x) Reorder the terms for easier multiplication: 0 = x(-4 + 4x)(5x + x2) Multiply (-4 + 4x) * (5x + x2) 0 = x(-4(5x + x2) + 4x * (5x + x2)) 0 = x((5x * -4 + x2 * -4) + 4x * (5x + x2)) 0 = x((-20x + -4x2) + 4x * (5x + x2)) 0 = x(-20x + -4x2 + (5x * 4x + x2 * 4x)) 0 = x(-20x + -4x2 + (20x2 + 4x3)) Combine like terms: -4x2 + 20x2 = 16x2 0 = x(-20x + 16x2 + 4x3) 0 = (-20x * x + 16x2 * x + 4x3 * x) 0 = (-20x2 + 16x3 + 4x4) Solving 0 = -20x2 + 16x3 + 4x4 Solving for variable 'x'. Remove the zero: 20x2 + -16x3 + -4x4 = -20x2 + 16x3 + 4x4 + 20x2 + -16x3 + -4x4 Reorder the terms: 20x2 + -16x3 + -4x4 = -20x2 + 20x2 + 16x3 + -16x3 + 4x4 + -4x4 Combine like terms: -20x2 + 20x2 = 0 20x2 + -16x3 + -4x4 = 0 + 16x3 + -16x3 + 4x4 + -4x4 20x2 + -16x3 + -4x4 = 16x3 + -16x3 + 4x4 + -4x4 Combine like terms: 16x3 + -16x3 = 0 20x2 + -16x3 + -4x4 = 0 + 4x4 + -4x4 20x2 + -16x3 + -4x4 = 4x4 + -4x4 Combine like terms: 4x4 + -4x4 = 0 20x2 + -16x3 + -4x4 = 0 Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(5 + -4x + -1x2) = 0 Factor a trinomial. 4x2((1 + -1x)(5 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
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 3
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0, 1, -5}
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