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Simplifying
(9m + 4n)(9m + -4n) = 0
Multiply (9m + 4n) * (9m + -4n)
(9m * (9m + -4n) + 4n * (9m + -4n)) = 0
((9m * 9m + -4n * 9m) + 4n * (9m + -4n)) = 0
Reorder the terms:
((-36mn + 81m2) + 4n * (9m + -4n)) = 0
((-36mn + 81m2) + 4n * (9m + -4n)) = 0
(-36mn + 81m2 + (9m * 4n + -4n * 4n)) = 0
(-36mn + 81m2 + (36mn + -16n2)) = 0
Reorder the terms:
(-36mn + 36mn + 81m2 + -16n2) = 0
Combine like terms: -36mn + 36mn = 0
(0 + 81m2 + -16n2) = 0
(81m2 + -16n2) = 0
Solving
81m2 + -16n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '16n2' to each side of the equation.
81m2 + -16n2 + 16n2 = 0 + 16n2
Combine like terms: -16n2 + 16n2 = 0
81m2 + 0 = 0 + 16n2
81m2 = 0 + 16n2
Remove the zero:
81m2 = 16n2
Divide each side by '81'.
m2 = 0.1975308642n2
Simplifying
m2 = 0.1975308642n2
Take the square root of each side:
m = {-0.444444444n, 0.444444444n}
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