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Simplifying 15m2 + 6mn + -21n2 = 0 Reorder the terms: 6mn + 15m2 + -21n2 = 0 Solving 6mn + 15m2 + -21n2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3'. 3(2mn + 5m2 + -7n2) = 0 Factor a trinomial. 3((m + -1n)(5m + 7n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(m + -1n)' equal to zero and attempt to solve: Simplifying m + -1n = 0 Solving m + -1n = 0 Move all terms containing m to the left, all other terms to the right. Add 'n' to each side of the equation. m + -1n + n = 0 + n Combine like terms: -1n + n = 0 m + 0 = 0 + n m = 0 + n Remove the zero: m = n Simplifying m = nSubproblem 2
Set the factor '(5m + 7n)' equal to zero and attempt to solve: Simplifying 5m + 7n = 0 Solving 5m + 7n = 0 Move all terms containing m to the left, all other terms to the right. Add '-7n' to each side of the equation. 5m + 7n + -7n = 0 + -7n Combine like terms: 7n + -7n = 0 5m + 0 = 0 + -7n 5m = 0 + -7n Remove the zero: 5m = -7n Divide each side by '5'. m = -1.4n Simplifying m = -1.4nSolution
m = {n, -1.4n}
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