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Simplifying
(3m + 8n)(3m + -8n) = 0
Multiply (3m + 8n) * (3m + -8n)
(3m * (3m + -8n) + 8n * (3m + -8n)) = 0
((3m * 3m + -8n * 3m) + 8n * (3m + -8n)) = 0
Reorder the terms:
((-24mn + 9m2) + 8n * (3m + -8n)) = 0
((-24mn + 9m2) + 8n * (3m + -8n)) = 0
(-24mn + 9m2 + (3m * 8n + -8n * 8n)) = 0
(-24mn + 9m2 + (24mn + -64n2)) = 0
Reorder the terms:
(-24mn + 24mn + 9m2 + -64n2) = 0
Combine like terms: -24mn + 24mn = 0
(0 + 9m2 + -64n2) = 0
(9m2 + -64n2) = 0
Solving
9m2 + -64n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '64n2' to each side of the equation.
9m2 + -64n2 + 64n2 = 0 + 64n2
Combine like terms: -64n2 + 64n2 = 0
9m2 + 0 = 0 + 64n2
9m2 = 0 + 64n2
Remove the zero:
9m2 = 64n2
Divide each side by '9'.
m2 = 7.111111111n2
Simplifying
m2 = 7.111111111n2
Take the square root of each side:
m = {-2.666666667n, 2.666666667n}
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