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Simplifying (x + 1)(3x + 7) + -1(x + 1)(x + -3) = 0 Reorder the terms: (1 + x)(3x + 7) + -1(x + 1)(x + -3) = 0 Reorder the terms: (1 + x)(7 + 3x) + -1(x + 1)(x + -3) = 0 Multiply (1 + x) * (7 + 3x) (1(7 + 3x) + x(7 + 3x)) + -1(x + 1)(x + -3) = 0 ((7 * 1 + 3x * 1) + x(7 + 3x)) + -1(x + 1)(x + -3) = 0 ((7 + 3x) + x(7 + 3x)) + -1(x + 1)(x + -3) = 0 (7 + 3x + (7 * x + 3x * x)) + -1(x + 1)(x + -3) = 0 (7 + 3x + (7x + 3x2)) + -1(x + 1)(x + -3) = 0 Combine like terms: 3x + 7x = 10x (7 + 10x + 3x2) + -1(x + 1)(x + -3) = 0 Reorder the terms: 7 + 10x + 3x2 + -1(1 + x)(x + -3) = 0 Reorder the terms: 7 + 10x + 3x2 + -1(1 + x)(-3 + x) = 0 Multiply (1 + x) * (-3 + x) 7 + 10x + 3x2 + -1(1(-3 + x) + x(-3 + x)) = 0 7 + 10x + 3x2 + -1((-3 * 1 + x * 1) + x(-3 + x)) = 0 7 + 10x + 3x2 + -1((-3 + 1x) + x(-3 + x)) = 0 7 + 10x + 3x2 + -1(-3 + 1x + (-3 * x + x * x)) = 0 7 + 10x + 3x2 + -1(-3 + 1x + (-3x + x2)) = 0 Combine like terms: 1x + -3x = -2x 7 + 10x + 3x2 + -1(-3 + -2x + x2) = 0 7 + 10x + 3x2 + (-3 * -1 + -2x * -1 + x2 * -1) = 0 7 + 10x + 3x2 + (3 + 2x + -1x2) = 0 Reorder the terms: 7 + 3 + 10x + 2x + 3x2 + -1x2 = 0 Combine like terms: 7 + 3 = 10 10 + 10x + 2x + 3x2 + -1x2 = 0 Combine like terms: 10x + 2x = 12x 10 + 12x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 10 + 12x + 2x2 = 0 Solving 10 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 6x + x2) = 0 Factor a trinomial. 2((5 + x)(1 + x)) = 0 Ignore the factor 2.Subproblem 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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