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Simplifying (14 + -2x)(12 + -2x) = 48 Multiply (14 + -2x) * (12 + -2x) (14(12 + -2x) + -2x * (12 + -2x)) = 48 ((12 * 14 + -2x * 14) + -2x * (12 + -2x)) = 48 ((168 + -28x) + -2x * (12 + -2x)) = 48 (168 + -28x + (12 * -2x + -2x * -2x)) = 48 (168 + -28x + (-24x + 4x2)) = 48 Combine like terms: -28x + -24x = -52x (168 + -52x + 4x2) = 48 Solving 168 + -52x + 4x2 = 48 Solving for variable 'x'. Reorder the terms: 168 + -48 + -52x + 4x2 = 48 + -48 Combine like terms: 168 + -48 = 120 120 + -52x + 4x2 = 48 + -48 Combine like terms: 48 + -48 = 0 120 + -52x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(30 + -13x + x2) = 0 Factor a trinomial. 4((3 + -1x)(10 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {3, 10}
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