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Simplifying (x + -6)(x + -4) = (x + -1) + (x + -2) Reorder the terms: (-6 + x)(x + -4) = (x + -1) + (x + -2) Reorder the terms: (-6 + x)(-4 + x) = (x + -1) + (x + -2) Multiply (-6 + x) * (-4 + x) (-6(-4 + x) + x(-4 + x)) = (x + -1) + (x + -2) ((-4 * -6 + x * -6) + x(-4 + x)) = (x + -1) + (x + -2) ((24 + -6x) + x(-4 + x)) = (x + -1) + (x + -2) (24 + -6x + (-4 * x + x * x)) = (x + -1) + (x + -2) (24 + -6x + (-4x + x2)) = (x + -1) + (x + -2) Combine like terms: -6x + -4x = -10x (24 + -10x + x2) = (x + -1) + (x + -2) Reorder the terms: 24 + -10x + x2 = (-1 + x) + (x + -2) Remove parenthesis around (-1 + x) 24 + -10x + x2 = -1 + x + (x + -2) Reorder the terms: 24 + -10x + x2 = -1 + x + (-2 + x) Remove parenthesis around (-2 + x) 24 + -10x + x2 = -1 + x + -2 + x Reorder the terms: 24 + -10x + x2 = -1 + -2 + x + x Combine like terms: -1 + -2 = -3 24 + -10x + x2 = -3 + x + x Combine like terms: x + x = 2x 24 + -10x + x2 = -3 + 2x Solving 24 + -10x + x2 = -3 + 2x Solving for variable 'x'. Reorder the terms: 24 + 3 + -10x + -2x + x2 = -3 + 2x + 3 + -2x Combine like terms: 24 + 3 = 27 27 + -10x + -2x + x2 = -3 + 2x + 3 + -2x Combine like terms: -10x + -2x = -12x 27 + -12x + x2 = -3 + 2x + 3 + -2x Reorder the terms: 27 + -12x + x2 = -3 + 3 + 2x + -2x Combine like terms: -3 + 3 = 0 27 + -12x + x2 = 0 + 2x + -2x 27 + -12x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 27 + -12x + x2 = 0 Factor a trinomial. (3 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 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 = {3, 9}
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