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Simplifying (x + -4)(x + 3) = 18 Reorder the terms: (-4 + x)(x + 3) = 18 Reorder the terms: (-4 + x)(3 + x) = 18 Multiply (-4 + x) * (3 + x) (-4(3 + x) + x(3 + x)) = 18 ((3 * -4 + x * -4) + x(3 + x)) = 18 ((-12 + -4x) + x(3 + x)) = 18 (-12 + -4x + (3 * x + x * x)) = 18 (-12 + -4x + (3x + x2)) = 18 Combine like terms: -4x + 3x = -1x (-12 + -1x + x2) = 18 Solving -12 + -1x + x2 = 18 Solving for variable 'x'. Reorder the terms: -12 + -18 + -1x + x2 = 18 + -18 Combine like terms: -12 + -18 = -30 -30 + -1x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -30 + -1x + x2 = 0 Factor a trinomial. (-5 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-5, 6}
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