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Simplifying (3x + 4)(x + 1) = (x + 1)(2x + -1) Reorder the terms: (4 + 3x)(x + 1) = (x + 1)(2x + -1) Reorder the terms: (4 + 3x)(1 + x) = (x + 1)(2x + -1) Multiply (4 + 3x) * (1 + x) (4(1 + x) + 3x * (1 + x)) = (x + 1)(2x + -1) ((1 * 4 + x * 4) + 3x * (1 + x)) = (x + 1)(2x + -1) ((4 + 4x) + 3x * (1 + x)) = (x + 1)(2x + -1) (4 + 4x + (1 * 3x + x * 3x)) = (x + 1)(2x + -1) (4 + 4x + (3x + 3x2)) = (x + 1)(2x + -1) Combine like terms: 4x + 3x = 7x (4 + 7x + 3x2) = (x + 1)(2x + -1) Reorder the terms: 4 + 7x + 3x2 = (1 + x)(2x + -1) Reorder the terms: 4 + 7x + 3x2 = (1 + x)(-1 + 2x) Multiply (1 + x) * (-1 + 2x) 4 + 7x + 3x2 = (1(-1 + 2x) + x(-1 + 2x)) 4 + 7x + 3x2 = ((-1 * 1 + 2x * 1) + x(-1 + 2x)) 4 + 7x + 3x2 = ((-1 + 2x) + x(-1 + 2x)) 4 + 7x + 3x2 = (-1 + 2x + (-1 * x + 2x * x)) 4 + 7x + 3x2 = (-1 + 2x + (-1x + 2x2)) Combine like terms: 2x + -1x = 1x 4 + 7x + 3x2 = (-1 + 1x + 2x2) Solving 4 + 7x + 3x2 = -1 + 1x + 2x2 Solving for variable 'x'. Reorder the terms: 4 + 1 + 7x + -1x + 3x2 + -2x2 = -1 + 1x + 2x2 + 1 + -1x + -2x2 Combine like terms: 4 + 1 = 5 5 + 7x + -1x + 3x2 + -2x2 = -1 + 1x + 2x2 + 1 + -1x + -2x2 Combine like terms: 7x + -1x = 6x 5 + 6x + 3x2 + -2x2 = -1 + 1x + 2x2 + 1 + -1x + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 5 + 6x + 1x2 = -1 + 1x + 2x2 + 1 + -1x + -2x2 Reorder the terms: 5 + 6x + 1x2 = -1 + 1 + 1x + -1x + 2x2 + -2x2 Combine like terms: -1 + 1 = 0 5 + 6x + 1x2 = 0 + 1x + -1x + 2x2 + -2x2 5 + 6x + 1x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 5 + 6x + 1x2 = 0 + 2x2 + -2x2 5 + 6x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + 6x + 1x2 = 0 Factor a trinomial. (5 + x)(1 + x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {-5, -1}
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