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Simplifying 240 = (x + 4)(3x + 6) Reorder the terms: 240 = (4 + x)(3x + 6) Reorder the terms: 240 = (4 + x)(6 + 3x) Multiply (4 + x) * (6 + 3x) 240 = (4(6 + 3x) + x(6 + 3x)) 240 = ((6 * 4 + 3x * 4) + x(6 + 3x)) 240 = ((24 + 12x) + x(6 + 3x)) 240 = (24 + 12x + (6 * x + 3x * x)) 240 = (24 + 12x + (6x + 3x2)) Combine like terms: 12x + 6x = 18x 240 = (24 + 18x + 3x2) Solving 240 = 24 + 18x + 3x2 Solving for variable 'x'. Combine like terms: 240 + -24 = 216 216 + -18x + -3x2 = 24 + 18x + 3x2 + -24 + -18x + -3x2 Reorder the terms: 216 + -18x + -3x2 = 24 + -24 + 18x + -18x + 3x2 + -3x2 Combine like terms: 24 + -24 = 0 216 + -18x + -3x2 = 0 + 18x + -18x + 3x2 + -3x2 216 + -18x + -3x2 = 18x + -18x + 3x2 + -3x2 Combine like terms: 18x + -18x = 0 216 + -18x + -3x2 = 0 + 3x2 + -3x2 216 + -18x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 216 + -18x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(72 + -6x + -1x2) = 0 Factor a trinomial. 3((6 + -1x)(12 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Subproblem 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 = {6, -12}
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