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Simplifying
(3m + 4n)(3m + -4n) = 0
Multiply (3m + 4n) * (3m + -4n)
(3m * (3m + -4n) + 4n * (3m + -4n)) = 0
((3m * 3m + -4n * 3m) + 4n * (3m + -4n)) = 0
Reorder the terms:
((-12mn + 9m2) + 4n * (3m + -4n)) = 0
((-12mn + 9m2) + 4n * (3m + -4n)) = 0
(-12mn + 9m2 + (3m * 4n + -4n * 4n)) = 0
(-12mn + 9m2 + (12mn + -16n2)) = 0
Reorder the terms:
(-12mn + 12mn + 9m2 + -16n2) = 0
Combine like terms: -12mn + 12mn = 0
(0 + 9m2 + -16n2) = 0
(9m2 + -16n2) = 0
Solving
9m2 + -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.
9m2 + -16n2 + 16n2 = 0 + 16n2
Combine like terms: -16n2 + 16n2 = 0
9m2 + 0 = 0 + 16n2
9m2 = 0 + 16n2
Remove the zero:
9m2 = 16n2
Divide each side by '9'.
m2 = 1.777777778n2
Simplifying
m2 = 1.777777778n2
Take the square root of each side:
m = {-1.333333333n, 1.333333333n}
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