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Simplifying (7x + 35)(2x + 12) = 0 Reorder the terms: (35 + 7x)(2x + 12) = 0 Reorder the terms: (35 + 7x)(12 + 2x) = 0 Multiply (35 + 7x) * (12 + 2x) (35(12 + 2x) + 7x * (12 + 2x)) = 0 ((12 * 35 + 2x * 35) + 7x * (12 + 2x)) = 0 ((420 + 70x) + 7x * (12 + 2x)) = 0 (420 + 70x + (12 * 7x + 2x * 7x)) = 0 (420 + 70x + (84x + 14x2)) = 0 Combine like terms: 70x + 84x = 154x (420 + 154x + 14x2) = 0 Solving 420 + 154x + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '14'. 14(30 + 11x + x2) = 0 Factor a trinomial. 14((6 + x)(5 + x)) = 0 Ignore the factor 14.Subproblem 1
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 = -6Subproblem 2
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 = -5Solution
x = {-6, -5}
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