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Simplifying
(5m + -2n)(5m + 2n) = 0
Multiply (5m + -2n) * (5m + 2n)
(5m * (5m + 2n) + -2n * (5m + 2n)) = 0
((5m * 5m + 2n * 5m) + -2n * (5m + 2n)) = 0
Reorder the terms:
((10mn + 25m2) + -2n * (5m + 2n)) = 0
((10mn + 25m2) + -2n * (5m + 2n)) = 0
(10mn + 25m2 + (5m * -2n + 2n * -2n)) = 0
(10mn + 25m2 + (-10mn + -4n2)) = 0
Reorder the terms:
(10mn + -10mn + 25m2 + -4n2) = 0
Combine like terms: 10mn + -10mn = 0
(0 + 25m2 + -4n2) = 0
(25m2 + -4n2) = 0
Solving
25m2 + -4n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '4n2' to each side of the equation.
25m2 + -4n2 + 4n2 = 0 + 4n2
Combine like terms: -4n2 + 4n2 = 0
25m2 + 0 = 0 + 4n2
25m2 = 0 + 4n2
Remove the zero:
25m2 = 4n2
Divide each side by '25'.
m2 = 0.16n2
Simplifying
m2 = 0.16n2
Take the square root of each side:
m = {-0.4n, 0.4n}
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