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Simplifying
(4m + 7n)(4m + -7n) = 0
Multiply (4m + 7n) * (4m + -7n)
(4m * (4m + -7n) + 7n * (4m + -7n)) = 0
((4m * 4m + -7n * 4m) + 7n * (4m + -7n)) = 0
Reorder the terms:
((-28mn + 16m2) + 7n * (4m + -7n)) = 0
((-28mn + 16m2) + 7n * (4m + -7n)) = 0
(-28mn + 16m2 + (4m * 7n + -7n * 7n)) = 0
(-28mn + 16m2 + (28mn + -49n2)) = 0
Reorder the terms:
(-28mn + 28mn + 16m2 + -49n2) = 0
Combine like terms: -28mn + 28mn = 0
(0 + 16m2 + -49n2) = 0
(16m2 + -49n2) = 0
Solving
16m2 + -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.
16m2 + -49n2 + 49n2 = 0 + 49n2
Combine like terms: -49n2 + 49n2 = 0
16m2 + 0 = 0 + 49n2
16m2 = 0 + 49n2
Remove the zero:
16m2 = 49n2
Divide each side by '16'.
m2 = 3.0625n2
Simplifying
m2 = 3.0625n2
Take the square root of each side:
m = {-1.75n, 1.75n}
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