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Simplifying
(-1m + 5n)(-1m + -5n) = 0
Multiply (-1m + 5n) * (-1m + -5n)
(-1m * (-1m + -5n) + 5n * (-1m + -5n)) = 0
((-1m * -1m + -5n * -1m) + 5n * (-1m + -5n)) = 0
Reorder the terms:
((5mn + 1m2) + 5n * (-1m + -5n)) = 0
((5mn + 1m2) + 5n * (-1m + -5n)) = 0
(5mn + 1m2 + (-1m * 5n + -5n * 5n)) = 0
(5mn + 1m2 + (-5mn + -25n2)) = 0
Reorder the terms:
(5mn + -5mn + 1m2 + -25n2) = 0
Combine like terms: 5mn + -5mn = 0
(0 + 1m2 + -25n2) = 0
(1m2 + -25n2) = 0
Solving
1m2 + -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.
1m2 + -25n2 + 25n2 = 0 + 25n2
Combine like terms: -25n2 + 25n2 = 0
1m2 + 0 = 0 + 25n2
1m2 = 0 + 25n2
Remove the zero:
1m2 = 25n2
Divide each side by '1'.
m2 = 25n2
Simplifying
m2 = 25n2
Take the square root of each side:
m = {-5n, 5n}
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