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Simplifying (7 + -1x)(x + -12) = 6 Reorder the terms: (7 + -1x)(-12 + x) = 6 Multiply (7 + -1x) * (-12 + x) (7(-12 + x) + -1x * (-12 + x)) = 6 ((-12 * 7 + x * 7) + -1x * (-12 + x)) = 6 ((-84 + 7x) + -1x * (-12 + x)) = 6 (-84 + 7x + (-12 * -1x + x * -1x)) = 6 (-84 + 7x + (12x + -1x2)) = 6 Combine like terms: 7x + 12x = 19x (-84 + 19x + -1x2) = 6 Solving -84 + 19x + -1x2 = 6 Solving for variable 'x'. Reorder the terms: -84 + -6 + 19x + -1x2 = 6 + -6 Combine like terms: -84 + -6 = -90 -90 + 19x + -1x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -90 + 19x + -1x2 = 0 Factor a trinomial. (-10 + x)(9 + -1x) = 0Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 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 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10Subproblem 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 = {10, 9}
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