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Simplifying (2x + -10)(x + -6) = 24 Reorder the terms: (-10 + 2x)(x + -6) = 24 Reorder the terms: (-10 + 2x)(-6 + x) = 24 Multiply (-10 + 2x) * (-6 + x) (-10(-6 + x) + 2x * (-6 + x)) = 24 ((-6 * -10 + x * -10) + 2x * (-6 + x)) = 24 ((60 + -10x) + 2x * (-6 + x)) = 24 (60 + -10x + (-6 * 2x + x * 2x)) = 24 (60 + -10x + (-12x + 2x2)) = 24 Combine like terms: -10x + -12x = -22x (60 + -22x + 2x2) = 24 Solving 60 + -22x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: 60 + -24 + -22x + 2x2 = 24 + -24 Combine like terms: 60 + -24 = 36 36 + -22x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 36 + -22x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -11x + x2) = 0 Factor a trinomial. 2((2 + -1x)(9 + -1x)) = 0 Ignore the factor 2.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 '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {2, 9}
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