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Simplifying
(6m + -11n)(6m + 11n) = 0
Multiply (6m + -11n) * (6m + 11n)
(6m * (6m + 11n) + -11n * (6m + 11n)) = 0
((6m * 6m + 11n * 6m) + -11n * (6m + 11n)) = 0
Reorder the terms:
((66mn + 36m2) + -11n * (6m + 11n)) = 0
((66mn + 36m2) + -11n * (6m + 11n)) = 0
(66mn + 36m2 + (6m * -11n + 11n * -11n)) = 0
(66mn + 36m2 + (-66mn + -121n2)) = 0
Reorder the terms:
(66mn + -66mn + 36m2 + -121n2) = 0
Combine like terms: 66mn + -66mn = 0
(0 + 36m2 + -121n2) = 0
(36m2 + -121n2) = 0
Solving
36m2 + -121n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '121n2' to each side of the equation.
36m2 + -121n2 + 121n2 = 0 + 121n2
Combine like terms: -121n2 + 121n2 = 0
36m2 + 0 = 0 + 121n2
36m2 = 0 + 121n2
Remove the zero:
36m2 = 121n2
Divide each side by '36'.
m2 = 3.361111111n2
Simplifying
m2 = 3.361111111n2
Take the square root of each side:
m = {-1.833333333n, 1.833333333n}
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