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