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Simplifying
(8m + -5n)(8m + 5n) = 0
Multiply (8m + -5n) * (8m + 5n)
(8m * (8m + 5n) + -5n * (8m + 5n)) = 0
((8m * 8m + 5n * 8m) + -5n * (8m + 5n)) = 0
Reorder the terms:
((40mn + 64m2) + -5n * (8m + 5n)) = 0
((40mn + 64m2) + -5n * (8m + 5n)) = 0
(40mn + 64m2 + (8m * -5n + 5n * -5n)) = 0
(40mn + 64m2 + (-40mn + -25n2)) = 0
Reorder the terms:
(40mn + -40mn + 64m2 + -25n2) = 0
Combine like terms: 40mn + -40mn = 0
(0 + 64m2 + -25n2) = 0
(64m2 + -25n2) = 0
Solving
64m2 + -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.
64m2 + -25n2 + 25n2 = 0 + 25n2
Combine like terms: -25n2 + 25n2 = 0
64m2 + 0 = 0 + 25n2
64m2 = 0 + 25n2
Remove the zero:
64m2 = 25n2
Divide each side by '64'.
m2 = 0.390625n2
Simplifying
m2 = 0.390625n2
Take the square root of each side:
m = {-0.625n, 0.625n}
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