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Simplifying (m + 1)(2m + 7) = 3(m + 4) + -9 Reorder the terms: (1 + m)(2m + 7) = 3(m + 4) + -9 Reorder the terms: (1 + m)(7 + 2m) = 3(m + 4) + -9 Multiply (1 + m) * (7 + 2m) (1(7 + 2m) + m(7 + 2m)) = 3(m + 4) + -9 ((7 * 1 + 2m * 1) + m(7 + 2m)) = 3(m + 4) + -9 ((7 + 2m) + m(7 + 2m)) = 3(m + 4) + -9 (7 + 2m + (7 * m + 2m * m)) = 3(m + 4) + -9 (7 + 2m + (7m + 2m2)) = 3(m + 4) + -9 Combine like terms: 2m + 7m = 9m (7 + 9m + 2m2) = 3(m + 4) + -9 Reorder the terms: 7 + 9m + 2m2 = 3(4 + m) + -9 7 + 9m + 2m2 = (4 * 3 + m * 3) + -9 7 + 9m + 2m2 = (12 + 3m) + -9 Reorder the terms: 7 + 9m + 2m2 = 12 + -9 + 3m Combine like terms: 12 + -9 = 3 7 + 9m + 2m2 = 3 + 3m Solving 7 + 9m + 2m2 = 3 + 3m Solving for variable 'm'. Reorder the terms: 7 + -3 + 9m + -3m + 2m2 = 3 + 3m + -3 + -3m Combine like terms: 7 + -3 = 4 4 + 9m + -3m + 2m2 = 3 + 3m + -3 + -3m Combine like terms: 9m + -3m = 6m 4 + 6m + 2m2 = 3 + 3m + -3 + -3m Reorder the terms: 4 + 6m + 2m2 = 3 + -3 + 3m + -3m Combine like terms: 3 + -3 = 0 4 + 6m + 2m2 = 0 + 3m + -3m 4 + 6m + 2m2 = 3m + -3m Combine like terms: 3m + -3m = 0 4 + 6m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3m + m2) = 0 Factor a trinomial. 2((2 + m)(1 + m)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + m)' equal to zero and attempt to solve: Simplifying 2 + m = 0 Solving 2 + m = 0 Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 0 + -2 Combine like terms: 2 + -2 = 0 0 + m = 0 + -2 m = 0 + -2 Combine like terms: 0 + -2 = -2 m = -2 Simplifying m = -2Subproblem 2
Set the factor '(1 + m)' equal to zero and attempt to solve: Simplifying 1 + m = 0 Solving 1 + m = 0 Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 0 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0 + -1 m = 0 + -1 Combine like terms: 0 + -1 = -1 m = -1 Simplifying m = -1Solution
m = {-2, -1}
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