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Simplifying (3x + 1)(x + 1) = (5x + 11)(x + -1) Reorder the terms: (1 + 3x)(x + 1) = (5x + 11)(x + -1) Reorder the terms: (1 + 3x)(1 + x) = (5x + 11)(x + -1) Multiply (1 + 3x) * (1 + x) (1(1 + x) + 3x * (1 + x)) = (5x + 11)(x + -1) ((1 * 1 + x * 1) + 3x * (1 + x)) = (5x + 11)(x + -1) ((1 + 1x) + 3x * (1 + x)) = (5x + 11)(x + -1) (1 + 1x + (1 * 3x + x * 3x)) = (5x + 11)(x + -1) (1 + 1x + (3x + 3x2)) = (5x + 11)(x + -1) Combine like terms: 1x + 3x = 4x (1 + 4x + 3x2) = (5x + 11)(x + -1) Reorder the terms: 1 + 4x + 3x2 = (11 + 5x)(x + -1) Reorder the terms: 1 + 4x + 3x2 = (11 + 5x)(-1 + x) Multiply (11 + 5x) * (-1 + x) 1 + 4x + 3x2 = (11(-1 + x) + 5x * (-1 + x)) 1 + 4x + 3x2 = ((-1 * 11 + x * 11) + 5x * (-1 + x)) 1 + 4x + 3x2 = ((-11 + 11x) + 5x * (-1 + x)) 1 + 4x + 3x2 = (-11 + 11x + (-1 * 5x + x * 5x)) 1 + 4x + 3x2 = (-11 + 11x + (-5x + 5x2)) Combine like terms: 11x + -5x = 6x 1 + 4x + 3x2 = (-11 + 6x + 5x2) Solving 1 + 4x + 3x2 = -11 + 6x + 5x2 Solving for variable 'x'. Reorder the terms: 1 + 11 + 4x + -6x + 3x2 + -5x2 = -11 + 6x + 5x2 + 11 + -6x + -5x2 Combine like terms: 1 + 11 = 12 12 + 4x + -6x + 3x2 + -5x2 = -11 + 6x + 5x2 + 11 + -6x + -5x2 Combine like terms: 4x + -6x = -2x 12 + -2x + 3x2 + -5x2 = -11 + 6x + 5x2 + 11 + -6x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 12 + -2x + -2x2 = -11 + 6x + 5x2 + 11 + -6x + -5x2 Reorder the terms: 12 + -2x + -2x2 = -11 + 11 + 6x + -6x + 5x2 + -5x2 Combine like terms: -11 + 11 = 0 12 + -2x + -2x2 = 0 + 6x + -6x + 5x2 + -5x2 12 + -2x + -2x2 = 6x + -6x + 5x2 + -5x2 Combine like terms: 6x + -6x = 0 12 + -2x + -2x2 = 0 + 5x2 + -5x2 12 + -2x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 12 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -1x + -1x2) = 0 Factor a trinomial. 2((2 + -1x)(3 + x)) = 0 Ignore the factor 2.Subproblem 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 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {2, -3}
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