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Simplifying (2x + 12)(x + 7) = 0 Reorder the terms: (12 + 2x)(x + 7) = 0 Reorder the terms: (12 + 2x)(7 + x) = 0 Multiply (12 + 2x) * (7 + x) (12(7 + x) + 2x * (7 + x)) = 0 ((7 * 12 + x * 12) + 2x * (7 + x)) = 0 ((84 + 12x) + 2x * (7 + x)) = 0 (84 + 12x + (7 * 2x + x * 2x)) = 0 (84 + 12x + (14x + 2x2)) = 0 Combine like terms: 12x + 14x = 26x (84 + 26x + 2x2) = 0 Solving 84 + 26x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(42 + 13x + x2) = 0 Factor a trinomial. 2((7 + x)(6 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {-7, -6}
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