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Simplifying
(7m + 9n)(7m + -9n) = 0
Multiply (7m + 9n) * (7m + -9n)
(7m * (7m + -9n) + 9n * (7m + -9n)) = 0
((7m * 7m + -9n * 7m) + 9n * (7m + -9n)) = 0
Reorder the terms:
((-63mn + 49m2) + 9n * (7m + -9n)) = 0
((-63mn + 49m2) + 9n * (7m + -9n)) = 0
(-63mn + 49m2 + (7m * 9n + -9n * 9n)) = 0
(-63mn + 49m2 + (63mn + -81n2)) = 0
Reorder the terms:
(-63mn + 63mn + 49m2 + -81n2) = 0
Combine like terms: -63mn + 63mn = 0
(0 + 49m2 + -81n2) = 0
(49m2 + -81n2) = 0
Solving
49m2 + -81n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '81n2' to each side of the equation.
49m2 + -81n2 + 81n2 = 0 + 81n2
Combine like terms: -81n2 + 81n2 = 0
49m2 + 0 = 0 + 81n2
49m2 = 0 + 81n2
Remove the zero:
49m2 = 81n2
Divide each side by '49'.
m2 = 1.653061224n2
Simplifying
m2 = 1.653061224n2
Take the square root of each side:
m = {-1.285714286n, 1.285714286n}
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