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