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Simplifying
(9m + 5n)(9m + -5n) = 0
Multiply (9m + 5n) * (9m + -5n)
(9m * (9m + -5n) + 5n * (9m + -5n)) = 0
((9m * 9m + -5n * 9m) + 5n * (9m + -5n)) = 0
Reorder the terms:
((-45mn + 81m2) + 5n * (9m + -5n)) = 0
((-45mn + 81m2) + 5n * (9m + -5n)) = 0
(-45mn + 81m2 + (9m * 5n + -5n * 5n)) = 0
(-45mn + 81m2 + (45mn + -25n2)) = 0
Reorder the terms:
(-45mn + 45mn + 81m2 + -25n2) = 0
Combine like terms: -45mn + 45mn = 0
(0 + 81m2 + -25n2) = 0
(81m2 + -25n2) = 0
Solving
81m2 + -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.
81m2 + -25n2 + 25n2 = 0 + 25n2
Combine like terms: -25n2 + 25n2 = 0
81m2 + 0 = 0 + 25n2
81m2 = 0 + 25n2
Remove the zero:
81m2 = 25n2
Divide each side by '81'.
m2 = 0.3086419753n2
Simplifying
m2 = 0.3086419753n2
Take the square root of each side:
m = {-0.555555556n, 0.555555556n}
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