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Simplifying 192 = 4(x + 6)(x + 4) Reorder the terms: 192 = 4(6 + x)(x + 4) Reorder the terms: 192 = 4(6 + x)(4 + x) Multiply (6 + x) * (4 + x) 192 = 4(6(4 + x) + x(4 + x)) 192 = 4((4 * 6 + x * 6) + x(4 + x)) 192 = 4((24 + 6x) + x(4 + x)) 192 = 4(24 + 6x + (4 * x + x * x)) 192 = 4(24 + 6x + (4x + x2)) Combine like terms: 6x + 4x = 10x 192 = 4(24 + 10x + x2) 192 = (24 * 4 + 10x * 4 + x2 * 4) 192 = (96 + 40x + 4x2) Solving 192 = 96 + 40x + 4x2 Solving for variable 'x'. Combine like terms: 192 + -96 = 96 96 + -40x + -4x2 = 96 + 40x + 4x2 + -96 + -40x + -4x2 Reorder the terms: 96 + -40x + -4x2 = 96 + -96 + 40x + -40x + 4x2 + -4x2 Combine like terms: 96 + -96 = 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 + -1x2) = 0 Factor a trinomial. 4((2 + -1x)(12 + x)) = 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {2, -12}
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