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Simplifying (x + 3)(x + -2) = 84 Reorder the terms: (3 + x)(x + -2) = 84 Reorder the terms: (3 + x)(-2 + x) = 84 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) = 84 ((-2 * 3 + x * 3) + x(-2 + x)) = 84 ((-6 + 3x) + x(-2 + x)) = 84 (-6 + 3x + (-2 * x + x * x)) = 84 (-6 + 3x + (-2x + x2)) = 84 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) = 84 Solving -6 + 1x + x2 = 84 Solving for variable 'x'. Reorder the terms: -6 + -84 + 1x + x2 = 84 + -84 Combine like terms: -6 + -84 = -90 -90 + 1x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -90 + 1x + x2 = 0 Factor a trinomial. (-10 + -1x)(9 + -1x) = 0Subproblem 1
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 = -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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