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Simplifying (2x + -3)(x + -2) + 12x = 18 Reorder the terms: (-3 + 2x)(x + -2) + 12x = 18 Reorder the terms: (-3 + 2x)(-2 + x) + 12x = 18 Multiply (-3 + 2x) * (-2 + x) (-3(-2 + x) + 2x * (-2 + x)) + 12x = 18 ((-2 * -3 + x * -3) + 2x * (-2 + x)) + 12x = 18 ((6 + -3x) + 2x * (-2 + x)) + 12x = 18 (6 + -3x + (-2 * 2x + x * 2x)) + 12x = 18 (6 + -3x + (-4x + 2x2)) + 12x = 18 Combine like terms: -3x + -4x = -7x (6 + -7x + 2x2) + 12x = 18 Reorder the terms: 6 + -7x + 12x + 2x2 = 18 Combine like terms: -7x + 12x = 5x 6 + 5x + 2x2 = 18 Solving 6 + 5x + 2x2 = 18 Solving for variable 'x'. Reorder the terms: 6 + -18 + 5x + 2x2 = 18 + -18 Combine like terms: 6 + -18 = -12 -12 + 5x + 2x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -12 + 5x + 2x2 = 0 Factor a trinomial. (-4 + -1x)(3 + -2x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-4, 1.5}
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