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Simplifying
(2m + -5n)(2m + 5n) = 0
Multiply (2m + -5n) * (2m + 5n)
(2m * (2m + 5n) + -5n * (2m + 5n)) = 0
((2m * 2m + 5n * 2m) + -5n * (2m + 5n)) = 0
Reorder the terms:
((10mn + 4m2) + -5n * (2m + 5n)) = 0
((10mn + 4m2) + -5n * (2m + 5n)) = 0
(10mn + 4m2 + (2m * -5n + 5n * -5n)) = 0
(10mn + 4m2 + (-10mn + -25n2)) = 0
Reorder the terms:
(10mn + -10mn + 4m2 + -25n2) = 0
Combine like terms: 10mn + -10mn = 0
(0 + 4m2 + -25n2) = 0
(4m2 + -25n2) = 0
Solving
4m2 + -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.
4m2 + -25n2 + 25n2 = 0 + 25n2
Combine like terms: -25n2 + 25n2 = 0
4m2 + 0 = 0 + 25n2
4m2 = 0 + 25n2
Remove the zero:
4m2 = 25n2
Divide each side by '4'.
m2 = 6.25n2
Simplifying
m2 = 6.25n2
Take the square root of each side:
m = {-2.5n, 2.5n}
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