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Simplifying
(8m + 3n)(8m + -3n) = 0
Multiply (8m + 3n) * (8m + -3n)
(8m * (8m + -3n) + 3n * (8m + -3n)) = 0
((8m * 8m + -3n * 8m) + 3n * (8m + -3n)) = 0
Reorder the terms:
((-24mn + 64m2) + 3n * (8m + -3n)) = 0
((-24mn + 64m2) + 3n * (8m + -3n)) = 0
(-24mn + 64m2 + (8m * 3n + -3n * 3n)) = 0
(-24mn + 64m2 + (24mn + -9n2)) = 0
Reorder the terms:
(-24mn + 24mn + 64m2 + -9n2) = 0
Combine like terms: -24mn + 24mn = 0
(0 + 64m2 + -9n2) = 0
(64m2 + -9n2) = 0
Solving
64m2 + -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.
64m2 + -9n2 + 9n2 = 0 + 9n2
Combine like terms: -9n2 + 9n2 = 0
64m2 + 0 = 0 + 9n2
64m2 = 0 + 9n2
Remove the zero:
64m2 = 9n2
Divide each side by '64'.
m2 = 0.140625n2
Simplifying
m2 = 0.140625n2
Take the square root of each side:
m = {-0.375n, 0.375n}
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