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Simplifying (x + 5) + -1(x + 3)(x + 5) = 0 Reorder the terms: (5 + x) + -1(x + 3)(x + 5) = 0 Remove parenthesis around (5 + x) 5 + x + -1(x + 3)(x + 5) = 0 Reorder the terms: 5 + x + -1(3 + x)(x + 5) = 0 Reorder the terms: 5 + x + -1(3 + x)(5 + x) = 0 Multiply (3 + x) * (5 + x) 5 + x + -1(3(5 + x) + x(5 + x)) = 0 5 + x + -1((5 * 3 + x * 3) + x(5 + x)) = 0 5 + x + -1((15 + 3x) + x(5 + x)) = 0 5 + x + -1(15 + 3x + (5 * x + x * x)) = 0 5 + x + -1(15 + 3x + (5x + x2)) = 0 Combine like terms: 3x + 5x = 8x 5 + x + -1(15 + 8x + x2) = 0 5 + x + (15 * -1 + 8x * -1 + x2 * -1) = 0 5 + x + (-15 + -8x + -1x2) = 0 Reorder the terms: 5 + -15 + x + -8x + -1x2 = 0 Combine like terms: 5 + -15 = -10 -10 + x + -8x + -1x2 = 0 Combine like terms: x + -8x = -7x -10 + -7x + -1x2 = 0 Solving -10 + -7x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 7x + x2) = 0 Factor a trinomial. -1((5 + x)(2 + x)) = 0 Ignore the factor -1.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-5, -2}
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