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Simplifying (2x + 3)(x + 1) + -1(x + -1)(x + 5) = 28 Reorder the terms: (3 + 2x)(x + 1) + -1(x + -1)(x + 5) = 28 Reorder the terms: (3 + 2x)(1 + x) + -1(x + -1)(x + 5) = 28 Multiply (3 + 2x) * (1 + x) (3(1 + x) + 2x * (1 + x)) + -1(x + -1)(x + 5) = 28 ((1 * 3 + x * 3) + 2x * (1 + x)) + -1(x + -1)(x + 5) = 28 ((3 + 3x) + 2x * (1 + x)) + -1(x + -1)(x + 5) = 28 (3 + 3x + (1 * 2x + x * 2x)) + -1(x + -1)(x + 5) = 28 (3 + 3x + (2x + 2x2)) + -1(x + -1)(x + 5) = 28 Combine like terms: 3x + 2x = 5x (3 + 5x + 2x2) + -1(x + -1)(x + 5) = 28 Reorder the terms: 3 + 5x + 2x2 + -1(-1 + x)(x + 5) = 28 Reorder the terms: 3 + 5x + 2x2 + -1(-1 + x)(5 + x) = 28 Multiply (-1 + x) * (5 + x) 3 + 5x + 2x2 + -1(-1(5 + x) + x(5 + x)) = 28 3 + 5x + 2x2 + -1((5 * -1 + x * -1) + x(5 + x)) = 28 3 + 5x + 2x2 + -1((-5 + -1x) + x(5 + x)) = 28 3 + 5x + 2x2 + -1(-5 + -1x + (5 * x + x * x)) = 28 3 + 5x + 2x2 + -1(-5 + -1x + (5x + x2)) = 28 Combine like terms: -1x + 5x = 4x 3 + 5x + 2x2 + -1(-5 + 4x + x2) = 28 3 + 5x + 2x2 + (-5 * -1 + 4x * -1 + x2 * -1) = 28 3 + 5x + 2x2 + (5 + -4x + -1x2) = 28 Reorder the terms: 3 + 5 + 5x + -4x + 2x2 + -1x2 = 28 Combine like terms: 3 + 5 = 8 8 + 5x + -4x + 2x2 + -1x2 = 28 Combine like terms: 5x + -4x = 1x 8 + 1x + 2x2 + -1x2 = 28 Combine like terms: 2x2 + -1x2 = 1x2 8 + 1x + 1x2 = 28 Solving 8 + 1x + 1x2 = 28 Solving for variable 'x'. Reorder the terms: 8 + -28 + 1x + 1x2 = 28 + -28 Combine like terms: 8 + -28 = -20 -20 + 1x + 1x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -20 + 1x + 1x2 = 0 Factor a trinomial. (-5 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
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 = 4Solution
x = {-5, 4}
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