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Simplifying (x + 3)(x + 5) + (x + 3)(x + 3) = 0 Reorder the terms: (3 + x)(x + 5) + (x + 3)(x + 3) = 0 Reorder the terms: (3 + x)(5 + x) + (x + 3)(x + 3) = 0 Multiply (3 + x) * (5 + x) (3(5 + x) + x(5 + x)) + (x + 3)(x + 3) = 0 ((5 * 3 + x * 3) + x(5 + x)) + (x + 3)(x + 3) = 0 ((15 + 3x) + x(5 + x)) + (x + 3)(x + 3) = 0 (15 + 3x + (5 * x + x * x)) + (x + 3)(x + 3) = 0 (15 + 3x + (5x + x2)) + (x + 3)(x + 3) = 0 Combine like terms: 3x + 5x = 8x (15 + 8x + x2) + (x + 3)(x + 3) = 0 Reorder the terms: 15 + 8x + x2 + (3 + x)(x + 3) = 0 Reorder the terms: 15 + 8x + x2 + (3 + x)(3 + x) = 0 Multiply (3 + x) * (3 + x) 15 + 8x + x2 + (3(3 + x) + x(3 + x)) = 0 15 + 8x + x2 + ((3 * 3 + x * 3) + x(3 + x)) = 0 15 + 8x + x2 + ((9 + 3x) + x(3 + x)) = 0 15 + 8x + x2 + (9 + 3x + (3 * x + x * x)) = 0 15 + 8x + x2 + (9 + 3x + (3x + x2)) = 0 Combine like terms: 3x + 3x = 6x 15 + 8x + x2 + (9 + 6x + x2) = 0 Reorder the terms: 15 + 9 + 8x + 6x + x2 + x2 = 0 Combine like terms: 15 + 9 = 24 24 + 8x + 6x + x2 + x2 = 0 Combine like terms: 8x + 6x = 14x 24 + 14x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 24 + 14x + 2x2 = 0 Solving 24 + 14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 7x + x2) = 0 Factor a trinomial. 2((4 + x)(3 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 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 = {-4, -3}
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