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Simplifying 14m4 + 30m2n2 + -36n4 = 0 Reorder the terms: 30m2n2 + 14m4 + -36n4 = 0 Solving 30m2n2 + 14m4 + -36n4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(15m2n2 + 7m4 + -18n4) = 0 Factor a trinomial. 2((7m2 + -6n2)(m2 + 3n2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7m2 + -6n2)' equal to zero and attempt to solve: Simplifying 7m2 + -6n2 = 0 Solving 7m2 + -6n2 = 0 Move all terms containing m to the left, all other terms to the right. Add '6n2' to each side of the equation. 7m2 + -6n2 + 6n2 = 0 + 6n2 Combine like terms: -6n2 + 6n2 = 0 7m2 + 0 = 0 + 6n2 7m2 = 0 + 6n2 Remove the zero: 7m2 = 6n2 Divide each side by '7'. m2 = 0.8571428571n2 Simplifying m2 = 0.8571428571n2 Take the square root of each side: m = {-0.9258201n, 0.9258201n}Subproblem 2
Set the factor '(m2 + 3n2)' equal to zero and attempt to solve: Simplifying m2 + 3n2 = 0 Solving m2 + 3n2 = 0 Move all terms containing m to the left, all other terms to the right. Add '-3n2' to each side of the equation. m2 + 3n2 + -3n2 = 0 + -3n2 Combine like terms: 3n2 + -3n2 = 0 m2 + 0 = 0 + -3n2 m2 = 0 + -3n2 Remove the zero: m2 = -3n2 Simplifying m2 = -3n2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
m = {-0.9258201n, 0.9258201n}
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