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Simplifying (2x + -6)(x + 2) = 5(x + -1) + -12 Reorder the terms: (-6 + 2x)(x + 2) = 5(x + -1) + -12 Reorder the terms: (-6 + 2x)(2 + x) = 5(x + -1) + -12 Multiply (-6 + 2x) * (2 + x) (-6(2 + x) + 2x * (2 + x)) = 5(x + -1) + -12 ((2 * -6 + x * -6) + 2x * (2 + x)) = 5(x + -1) + -12 ((-12 + -6x) + 2x * (2 + x)) = 5(x + -1) + -12 (-12 + -6x + (2 * 2x + x * 2x)) = 5(x + -1) + -12 (-12 + -6x + (4x + 2x2)) = 5(x + -1) + -12 Combine like terms: -6x + 4x = -2x (-12 + -2x + 2x2) = 5(x + -1) + -12 Reorder the terms: -12 + -2x + 2x2 = 5(-1 + x) + -12 -12 + -2x + 2x2 = (-1 * 5 + x * 5) + -12 -12 + -2x + 2x2 = (-5 + 5x) + -12 Reorder the terms: -12 + -2x + 2x2 = -5 + -12 + 5x Combine like terms: -5 + -12 = -17 -12 + -2x + 2x2 = -17 + 5x Solving -12 + -2x + 2x2 = -17 + 5x Solving for variable 'x'. Reorder the terms: -12 + 17 + -2x + -5x + 2x2 = -17 + 5x + 17 + -5x Combine like terms: -12 + 17 = 5 5 + -2x + -5x + 2x2 = -17 + 5x + 17 + -5x Combine like terms: -2x + -5x = -7x 5 + -7x + 2x2 = -17 + 5x + 17 + -5x Reorder the terms: 5 + -7x + 2x2 = -17 + 17 + 5x + -5x Combine like terms: -17 + 17 = 0 5 + -7x + 2x2 = 0 + 5x + -5x 5 + -7x + 2x2 = 5x + -5x Combine like terms: 5x + -5x = 0 5 + -7x + 2x2 = 0 Factor a trinomial. (1 + -1x)(5 + -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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {1, 2.5}
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