20m^2-7mn-6n^2=0

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Solution for 20m^2-7mn-6n^2=0 equation:


Simplifying
20m2 + -7mn + -6n2 = 0

Reorder the terms:
-7mn + 20m2 + -6n2 = 0

Solving
-7mn + 20m2 + -6n2 = 0

Solving for variable 'm'.

Factor a trinomial.
(4m + -3n)(5m + 2n) = 0

Subproblem 1

Set the factor '(4m + -3n)' equal to zero and attempt to solve: Simplifying 4m + -3n = 0 Solving 4m + -3n = 0 Move all terms containing m to the left, all other terms to the right. Add '3n' to each side of the equation. 4m + -3n + 3n = 0 + 3n Combine like terms: -3n + 3n = 0 4m + 0 = 0 + 3n 4m = 0 + 3n Remove the zero: 4m = 3n Divide each side by '4'. m = 0.75n Simplifying m = 0.75n

Subproblem 2

Set the factor '(5m + 2n)' equal to zero and attempt to solve: Simplifying 5m + 2n = 0 Solving 5m + 2n = 0 Move all terms containing m to the left, all other terms to the right. Add '-2n' to each side of the equation. 5m + 2n + -2n = 0 + -2n Combine like terms: 2n + -2n = 0 5m + 0 = 0 + -2n 5m = 0 + -2n Remove the zero: 5m = -2n Divide each side by '5'. m = -0.4n Simplifying m = -0.4n

Solution

m = {0.75n, -0.4n}

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