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Simplifying
(7m + 5n)(7m + -5n) = 0
Multiply (7m + 5n) * (7m + -5n)
(7m * (7m + -5n) + 5n * (7m + -5n)) = 0
((7m * 7m + -5n * 7m) + 5n * (7m + -5n)) = 0
Reorder the terms:
((-35mn + 49m2) + 5n * (7m + -5n)) = 0
((-35mn + 49m2) + 5n * (7m + -5n)) = 0
(-35mn + 49m2 + (7m * 5n + -5n * 5n)) = 0
(-35mn + 49m2 + (35mn + -25n2)) = 0
Reorder the terms:
(-35mn + 35mn + 49m2 + -25n2) = 0
Combine like terms: -35mn + 35mn = 0
(0 + 49m2 + -25n2) = 0
(49m2 + -25n2) = 0
Solving
49m2 + -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.
49m2 + -25n2 + 25n2 = 0 + 25n2
Combine like terms: -25n2 + 25n2 = 0
49m2 + 0 = 0 + 25n2
49m2 = 0 + 25n2
Remove the zero:
49m2 = 25n2
Divide each side by '49'.
m2 = 0.5102040816n2
Simplifying
m2 = 0.5102040816n2
Take the square root of each side:
m = {-0.714285714n, 0.714285714n}
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