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Simplifying (2x + 6)(x + 3) + (12x + 36) = 0 Reorder the terms: (6 + 2x)(x + 3) + (12x + 36) = 0 Reorder the terms: (6 + 2x)(3 + x) + (12x + 36) = 0 Multiply (6 + 2x) * (3 + x) (6(3 + x) + 2x * (3 + x)) + (12x + 36) = 0 ((3 * 6 + x * 6) + 2x * (3 + x)) + (12x + 36) = 0 ((18 + 6x) + 2x * (3 + x)) + (12x + 36) = 0 (18 + 6x + (3 * 2x + x * 2x)) + (12x + 36) = 0 (18 + 6x + (6x + 2x2)) + (12x + 36) = 0 Combine like terms: 6x + 6x = 12x (18 + 12x + 2x2) + (12x + 36) = 0 Reorder the terms: 18 + 12x + 2x2 + (36 + 12x) = 0 Remove parenthesis around (36 + 12x) 18 + 12x + 2x2 + 36 + 12x = 0 Reorder the terms: 18 + 36 + 12x + 12x + 2x2 = 0 Combine like terms: 18 + 36 = 54 54 + 12x + 12x + 2x2 = 0 Combine like terms: 12x + 12x = 24x 54 + 24x + 2x2 = 0 Solving 54 + 24x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 12x + x2) = 0 Factor a trinomial. 2((9 + x)(3 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 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 = {-9, -3}
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