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Simplifying
(5m + 7n)(5m + -7n) = 0
Multiply (5m + 7n) * (5m + -7n)
(5m * (5m + -7n) + 7n * (5m + -7n)) = 0
((5m * 5m + -7n * 5m) + 7n * (5m + -7n)) = 0
Reorder the terms:
((-35mn + 25m2) + 7n * (5m + -7n)) = 0
((-35mn + 25m2) + 7n * (5m + -7n)) = 0
(-35mn + 25m2 + (5m * 7n + -7n * 7n)) = 0
(-35mn + 25m2 + (35mn + -49n2)) = 0
Reorder the terms:
(-35mn + 35mn + 25m2 + -49n2) = 0
Combine like terms: -35mn + 35mn = 0
(0 + 25m2 + -49n2) = 0
(25m2 + -49n2) = 0
Solving
25m2 + -49n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '49n2' to each side of the equation.
25m2 + -49n2 + 49n2 = 0 + 49n2
Combine like terms: -49n2 + 49n2 = 0
25m2 + 0 = 0 + 49n2
25m2 = 0 + 49n2
Remove the zero:
25m2 = 49n2
Divide each side by '25'.
m2 = 1.96n2
Simplifying
m2 = 1.96n2
Take the square root of each side:
m = {-1.4n, 1.4n}
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