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Simplifying
(4m + 3n)(4m + -3n) = 0
Multiply (4m + 3n) * (4m + -3n)
(4m * (4m + -3n) + 3n * (4m + -3n)) = 0
((4m * 4m + -3n * 4m) + 3n * (4m + -3n)) = 0
Reorder the terms:
((-12mn + 16m2) + 3n * (4m + -3n)) = 0
((-12mn + 16m2) + 3n * (4m + -3n)) = 0
(-12mn + 16m2 + (4m * 3n + -3n * 3n)) = 0
(-12mn + 16m2 + (12mn + -9n2)) = 0
Reorder the terms:
(-12mn + 12mn + 16m2 + -9n2) = 0
Combine like terms: -12mn + 12mn = 0
(0 + 16m2 + -9n2) = 0
(16m2 + -9n2) = 0
Solving
16m2 + -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.
16m2 + -9n2 + 9n2 = 0 + 9n2
Combine like terms: -9n2 + 9n2 = 0
16m2 + 0 = 0 + 9n2
16m2 = 0 + 9n2
Remove the zero:
16m2 = 9n2
Divide each side by '16'.
m2 = 0.5625n2
Simplifying
m2 = 0.5625n2
Take the square root of each side:
m = {-0.75n, 0.75n}
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