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Simplifying (x + -3)(x + -4) = 30 Reorder the terms: (-3 + x)(x + -4) = 30 Reorder the terms: (-3 + x)(-4 + x) = 30 Multiply (-3 + x) * (-4 + x) (-3(-4 + x) + x(-4 + x)) = 30 ((-4 * -3 + x * -3) + x(-4 + x)) = 30 ((12 + -3x) + x(-4 + x)) = 30 (12 + -3x + (-4 * x + x * x)) = 30 (12 + -3x + (-4x + x2)) = 30 Combine like terms: -3x + -4x = -7x (12 + -7x + x2) = 30 Solving 12 + -7x + x2 = 30 Solving for variable 'x'. Reorder the terms: 12 + -30 + -7x + x2 = 30 + -30 Combine like terms: 12 + -30 = -18 -18 + -7x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -18 + -7x + x2 = 0 Factor a trinomial. (-2 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 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 = {-2, 9}
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