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Simplifying 4 = (4x + 20)(x + 5) Reorder the terms: 4 = (20 + 4x)(x + 5) Reorder the terms: 4 = (20 + 4x)(5 + x) Multiply (20 + 4x) * (5 + x) 4 = (20(5 + x) + 4x * (5 + x)) 4 = ((5 * 20 + x * 20) + 4x * (5 + x)) 4 = ((100 + 20x) + 4x * (5 + x)) 4 = (100 + 20x + (5 * 4x + x * 4x)) 4 = (100 + 20x + (20x + 4x2)) Combine like terms: 20x + 20x = 40x 4 = (100 + 40x + 4x2) Solving 4 = 100 + 40x + 4x2 Solving for variable 'x'. Combine like terms: 4 + -100 = -96 -96 + -40x + -4x2 = 100 + 40x + 4x2 + -100 + -40x + -4x2 Reorder the terms: -96 + -40x + -4x2 = 100 + -100 + 40x + -40x + 4x2 + -4x2 Combine like terms: 100 + -100 = 0 -96 + -40x + -4x2 = 0 + 40x + -40x + 4x2 + -4x2 -96 + -40x + -4x2 = 40x + -40x + 4x2 + -4x2 Combine like terms: 40x + -40x = 0 -96 + -40x + -4x2 = 0 + 4x2 + -4x2 -96 + -40x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -96 + -40x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(24 + 10x + x2) = 0 Factor a trinomial. -4((6 + x)(4 + x)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-6, -4}
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