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Simplifying (2x + 48)(2x + 72) = 6912 Reorder the terms: (48 + 2x)(2x + 72) = 6912 Reorder the terms: (48 + 2x)(72 + 2x) = 6912 Multiply (48 + 2x) * (72 + 2x) (48(72 + 2x) + 2x * (72 + 2x)) = 6912 ((72 * 48 + 2x * 48) + 2x * (72 + 2x)) = 6912 ((3456 + 96x) + 2x * (72 + 2x)) = 6912 (3456 + 96x + (72 * 2x + 2x * 2x)) = 6912 (3456 + 96x + (144x + 4x2)) = 6912 Combine like terms: 96x + 144x = 240x (3456 + 240x + 4x2) = 6912 Solving 3456 + 240x + 4x2 = 6912 Solving for variable 'x'. Reorder the terms: 3456 + -6912 + 240x + 4x2 = 6912 + -6912 Combine like terms: 3456 + -6912 = -3456 -3456 + 240x + 4x2 = 6912 + -6912 Combine like terms: 6912 + -6912 = 0 -3456 + 240x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-864 + 60x + x2) = 0 Factor a trinomial. 4((-72 + -1x)(12 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-72 + -1x)' equal to zero and attempt to solve: Simplifying -72 + -1x = 0 Solving -72 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '72' to each side of the equation. -72 + 72 + -1x = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -1x = 0 + 72 -1x = 0 + 72 Combine like terms: 0 + 72 = 72 -1x = 72 Divide each side by '-1'. x = -72 Simplifying x = -72Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 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 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {-72, 12}
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