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Simplifying (x + -4)(x + -3) = 20 Reorder the terms: (-4 + x)(x + -3) = 20 Reorder the terms: (-4 + x)(-3 + x) = 20 Multiply (-4 + x) * (-3 + x) (-4(-3 + x) + x(-3 + x)) = 20 ((-3 * -4 + x * -4) + x(-3 + x)) = 20 ((12 + -4x) + x(-3 + x)) = 20 (12 + -4x + (-3 * x + x * x)) = 20 (12 + -4x + (-3x + x2)) = 20 Combine like terms: -4x + -3x = -7x (12 + -7x + x2) = 20 Solving 12 + -7x + x2 = 20 Solving for variable 'x'. Reorder the terms: 12 + -20 + -7x + x2 = 20 + -20 Combine like terms: 12 + -20 = -8 -8 + -7x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -8 + -7x + x2 = 0 Factor a trinomial. (-1 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-1, 8}
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