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Simplifying (3m + 1)(3m + 1) + 7(3m + 1) + 10 = 0 Reorder the terms: (1 + 3m)(3m + 1) + 7(3m + 1) + 10 = 0 Reorder the terms: (1 + 3m)(1 + 3m) + 7(3m + 1) + 10 = 0 Multiply (1 + 3m) * (1 + 3m) (1(1 + 3m) + 3m * (1 + 3m)) + 7(3m + 1) + 10 = 0 ((1 * 1 + 3m * 1) + 3m * (1 + 3m)) + 7(3m + 1) + 10 = 0 ((1 + 3m) + 3m * (1 + 3m)) + 7(3m + 1) + 10 = 0 (1 + 3m + (1 * 3m + 3m * 3m)) + 7(3m + 1) + 10 = 0 (1 + 3m + (3m + 9m2)) + 7(3m + 1) + 10 = 0 Combine like terms: 3m + 3m = 6m (1 + 6m + 9m2) + 7(3m + 1) + 10 = 0 Reorder the terms: 1 + 6m + 9m2 + 7(1 + 3m) + 10 = 0 1 + 6m + 9m2 + (1 * 7 + 3m * 7) + 10 = 0 1 + 6m + 9m2 + (7 + 21m) + 10 = 0 Reorder the terms: 1 + 7 + 10 + 6m + 21m + 9m2 = 0 Combine like terms: 1 + 7 = 8 8 + 10 + 6m + 21m + 9m2 = 0 Combine like terms: 8 + 10 = 18 18 + 6m + 21m + 9m2 = 0 Combine like terms: 6m + 21m = 27m 18 + 27m + 9m2 = 0 Solving 18 + 27m + 9m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '9'. 9(2 + 3m + m2) = 0 Factor a trinomial. 9((2 + m)(1 + m)) = 0 Ignore the factor 9.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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