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Simplifying
(5m + 3n)(5m + -3n) = 0
Multiply (5m + 3n) * (5m + -3n)
(5m * (5m + -3n) + 3n * (5m + -3n)) = 0
((5m * 5m + -3n * 5m) + 3n * (5m + -3n)) = 0
Reorder the terms:
((-15mn + 25m2) + 3n * (5m + -3n)) = 0
((-15mn + 25m2) + 3n * (5m + -3n)) = 0
(-15mn + 25m2 + (5m * 3n + -3n * 3n)) = 0
(-15mn + 25m2 + (15mn + -9n2)) = 0
Reorder the terms:
(-15mn + 15mn + 25m2 + -9n2) = 0
Combine like terms: -15mn + 15mn = 0
(0 + 25m2 + -9n2) = 0
(25m2 + -9n2) = 0
Solving
25m2 + -9n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '9n2' to each side of the equation.
25m2 + -9n2 + 9n2 = 0 + 9n2
Combine like terms: -9n2 + 9n2 = 0
25m2 + 0 = 0 + 9n2
25m2 = 0 + 9n2
Remove the zero:
25m2 = 9n2
Divide each side by '25'.
m2 = 0.36n2
Simplifying
m2 = 0.36n2
Take the square root of each side:
m = {-0.6n, 0.6n}
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