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Simplifying (x + -6)(x + -8) = 24 Reorder the terms: (-6 + x)(x + -8) = 24 Reorder the terms: (-6 + x)(-8 + x) = 24 Multiply (-6 + x) * (-8 + x) (-6(-8 + x) + x(-8 + x)) = 24 ((-8 * -6 + x * -6) + x(-8 + x)) = 24 ((48 + -6x) + x(-8 + x)) = 24 (48 + -6x + (-8 * x + x * x)) = 24 (48 + -6x + (-8x + x2)) = 24 Combine like terms: -6x + -8x = -14x (48 + -14x + x2) = 24 Solving 48 + -14x + x2 = 24 Solving for variable 'x'. Reorder the terms: 48 + -24 + -14x + x2 = 24 + -24 Combine like terms: 48 + -24 = 24 24 + -14x + x2 = 24 + -24 Combine like terms: 24 + -24 = 0 24 + -14x + x2 = 0 Factor a trinomial. (2 + -1x)(12 + -1x) = 0Subproblem 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 + -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 = {2, 12}
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