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Simplifying (x + -6)(x + -7) = 6 Reorder the terms: (-6 + x)(x + -7) = 6 Reorder the terms: (-6 + x)(-7 + x) = 6 Multiply (-6 + x) * (-7 + x) (-6(-7 + x) + x(-7 + x)) = 6 ((-7 * -6 + x * -6) + x(-7 + x)) = 6 ((42 + -6x) + x(-7 + x)) = 6 (42 + -6x + (-7 * x + x * x)) = 6 (42 + -6x + (-7x + x2)) = 6 Combine like terms: -6x + -7x = -13x (42 + -13x + x2) = 6 Solving 42 + -13x + x2 = 6 Solving for variable 'x'. Reorder the terms: 42 + -6 + -13x + x2 = 6 + -6 Combine like terms: 42 + -6 = 36 36 + -13x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 36 + -13x + x2 = 0 Factor a trinomial. (4 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 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 = {4, 9}
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