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Simplifying
(6m + 7n)(6m + -7n) = 0
Multiply (6m + 7n) * (6m + -7n)
(6m * (6m + -7n) + 7n * (6m + -7n)) = 0
((6m * 6m + -7n * 6m) + 7n * (6m + -7n)) = 0
Reorder the terms:
((-42mn + 36m2) + 7n * (6m + -7n)) = 0
((-42mn + 36m2) + 7n * (6m + -7n)) = 0
(-42mn + 36m2 + (6m * 7n + -7n * 7n)) = 0
(-42mn + 36m2 + (42mn + -49n2)) = 0
Reorder the terms:
(-42mn + 42mn + 36m2 + -49n2) = 0
Combine like terms: -42mn + 42mn = 0
(0 + 36m2 + -49n2) = 0
(36m2 + -49n2) = 0
Solving
36m2 + -49n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '49n2' to each side of the equation.
36m2 + -49n2 + 49n2 = 0 + 49n2
Combine like terms: -49n2 + 49n2 = 0
36m2 + 0 = 0 + 49n2
36m2 = 0 + 49n2
Remove the zero:
36m2 = 49n2
Divide each side by '36'.
m2 = 1.361111111n2
Simplifying
m2 = 1.361111111n2
Take the square root of each side:
m = {-1.166666667n, 1.166666667n}
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