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Simplifying 2(x + 3)(x + -1) = x(x + 3) + 84 Reorder the terms: 2(3 + x)(x + -1) = x(x + 3) + 84 Reorder the terms: 2(3 + x)(-1 + x) = x(x + 3) + 84 Multiply (3 + x) * (-1 + x) 2(3(-1 + x) + x(-1 + x)) = x(x + 3) + 84 2((-1 * 3 + x * 3) + x(-1 + x)) = x(x + 3) + 84 2((-3 + 3x) + x(-1 + x)) = x(x + 3) + 84 2(-3 + 3x + (-1 * x + x * x)) = x(x + 3) + 84 2(-3 + 3x + (-1x + x2)) = x(x + 3) + 84 Combine like terms: 3x + -1x = 2x 2(-3 + 2x + x2) = x(x + 3) + 84 (-3 * 2 + 2x * 2 + x2 * 2) = x(x + 3) + 84 (-6 + 4x + 2x2) = x(x + 3) + 84 Reorder the terms: -6 + 4x + 2x2 = x(3 + x) + 84 -6 + 4x + 2x2 = (3 * x + x * x) + 84 -6 + 4x + 2x2 = (3x + x2) + 84 Reorder the terms: -6 + 4x + 2x2 = 84 + 3x + x2 Solving -6 + 4x + 2x2 = 84 + 3x + x2 Solving for variable 'x'. Reorder the terms: -6 + -84 + 4x + -3x + 2x2 + -1x2 = 84 + 3x + x2 + -84 + -3x + -1x2 Combine like terms: -6 + -84 = -90 -90 + 4x + -3x + 2x2 + -1x2 = 84 + 3x + x2 + -84 + -3x + -1x2 Combine like terms: 4x + -3x = 1x -90 + 1x + 2x2 + -1x2 = 84 + 3x + x2 + -84 + -3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -90 + 1x + 1x2 = 84 + 3x + x2 + -84 + -3x + -1x2 Reorder the terms: -90 + 1x + 1x2 = 84 + -84 + 3x + -3x + x2 + -1x2 Combine like terms: 84 + -84 = 0 -90 + 1x + 1x2 = 0 + 3x + -3x + x2 + -1x2 -90 + 1x + 1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 -90 + 1x + 1x2 = 0 + x2 + -1x2 -90 + 1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -90 + 1x + 1x2 = 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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