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Simplifying
(6m + 5n)(6m + -5n) = 0
Multiply (6m + 5n) * (6m + -5n)
(6m * (6m + -5n) + 5n * (6m + -5n)) = 0
((6m * 6m + -5n * 6m) + 5n * (6m + -5n)) = 0
Reorder the terms:
((-30mn + 36m2) + 5n * (6m + -5n)) = 0
((-30mn + 36m2) + 5n * (6m + -5n)) = 0
(-30mn + 36m2 + (6m * 5n + -5n * 5n)) = 0
(-30mn + 36m2 + (30mn + -25n2)) = 0
Reorder the terms:
(-30mn + 30mn + 36m2 + -25n2) = 0
Combine like terms: -30mn + 30mn = 0
(0 + 36m2 + -25n2) = 0
(36m2 + -25n2) = 0
Solving
36m2 + -25n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '25n2' to each side of the equation.
36m2 + -25n2 + 25n2 = 0 + 25n2
Combine like terms: -25n2 + 25n2 = 0
36m2 + 0 = 0 + 25n2
36m2 = 0 + 25n2
Remove the zero:
36m2 = 25n2
Divide each side by '36'.
m2 = 0.6944444444n2
Simplifying
m2 = 0.6944444444n2
Take the square root of each side:
m = {-0.833333333n, 0.833333333n}
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