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Simplifying (2x + -1)(x + -3) = 12 Reorder the terms: (-1 + 2x)(x + -3) = 12 Reorder the terms: (-1 + 2x)(-3 + x) = 12 Multiply (-1 + 2x) * (-3 + x) (-1(-3 + x) + 2x * (-3 + x)) = 12 ((-3 * -1 + x * -1) + 2x * (-3 + x)) = 12 ((3 + -1x) + 2x * (-3 + x)) = 12 (3 + -1x + (-3 * 2x + x * 2x)) = 12 (3 + -1x + (-6x + 2x2)) = 12 Combine like terms: -1x + -6x = -7x (3 + -7x + 2x2) = 12 Solving 3 + -7x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: 3 + -12 + -7x + 2x2 = 12 + -12 Combine like terms: 3 + -12 = -9 -9 + -7x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -9 + -7x + 2x2 = 0 Factor a trinomial. (-1 + -1x)(9 + -2x) = 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 '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 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 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Solution
x = {-1, 4.5}
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