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Simplifying (3m + n)(3m + n) = 0 Multiply (3m + n) * (3m + n) (3m * (3m + n) + n(3m + n)) = 0 ((3m * 3m + n * 3m) + n(3m + n)) = 0 Reorder the terms: ((3mn + 9m2) + n(3m + n)) = 0 ((3mn + 9m2) + n(3m + n)) = 0 (3mn + 9m2 + (3m * n + n * n)) = 0 (3mn + 9m2 + (3mn + n2)) = 0 Reorder the terms: (3mn + 3mn + 9m2 + n2) = 0 Combine like terms: 3mn + 3mn = 6mn (6mn + 9m2 + n2) = 0 Solving 6mn + 9m2 + n2 = 0 Solving for variable 'm'. Factor a trinomial. (3m + n)(3m + n) = 0Subproblem 1
Set the factor '(3m + n)' equal to zero and attempt to solve: Simplifying 3m + n = 0 Solving 3m + n = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n' to each side of the equation. 3m + n + -1n = 0 + -1n Combine like terms: n + -1n = 0 3m + 0 = 0 + -1n 3m = 0 + -1n Remove the zero: 3m = -1n Divide each side by '3'. m = -0.3333333333n Simplifying m = -0.3333333333nSubproblem 2
Set the factor '(3m + n)' equal to zero and attempt to solve: Simplifying 3m + n = 0 Solving 3m + n = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n' to each side of the equation. 3m + n + -1n = 0 + -1n Combine like terms: n + -1n = 0 3m + 0 = 0 + -1n 3m = 0 + -1n Remove the zero: 3m = -1n Divide each side by '3'. m = -0.3333333333n Simplifying m = -0.3333333333nSolution
m = {-0.3333333333n, -0.3333333333n}
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