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Simplifying (2x + -3)(x + -4) = 18 Reorder the terms: (-3 + 2x)(x + -4) = 18 Reorder the terms: (-3 + 2x)(-4 + x) = 18 Multiply (-3 + 2x) * (-4 + x) (-3(-4 + x) + 2x * (-4 + x)) = 18 ((-4 * -3 + x * -3) + 2x * (-4 + x)) = 18 ((12 + -3x) + 2x * (-4 + x)) = 18 (12 + -3x + (-4 * 2x + x * 2x)) = 18 (12 + -3x + (-8x + 2x2)) = 18 Combine like terms: -3x + -8x = -11x (12 + -11x + 2x2) = 18 Solving 12 + -11x + 2x2 = 18 Solving for variable 'x'. Reorder the terms: 12 + -18 + -11x + 2x2 = 18 + -18 Combine like terms: 12 + -18 = -6 -6 + -11x + 2x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -6 + -11x + 2x2 = 0 Factor a trinomial. (-1 + -2x)(6 + -1x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 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 = {-0.5, 6}
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