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Simplifying
(7m + 4n)(7m + -4n) = 0
Multiply (7m + 4n) * (7m + -4n)
(7m * (7m + -4n) + 4n * (7m + -4n)) = 0
((7m * 7m + -4n * 7m) + 4n * (7m + -4n)) = 0
Reorder the terms:
((-28mn + 49m2) + 4n * (7m + -4n)) = 0
((-28mn + 49m2) + 4n * (7m + -4n)) = 0
(-28mn + 49m2 + (7m * 4n + -4n * 4n)) = 0
(-28mn + 49m2 + (28mn + -16n2)) = 0
Reorder the terms:
(-28mn + 28mn + 49m2 + -16n2) = 0
Combine like terms: -28mn + 28mn = 0
(0 + 49m2 + -16n2) = 0
(49m2 + -16n2) = 0
Solving
49m2 + -16n2 = 0
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '16n2' to each side of the equation.
49m2 + -16n2 + 16n2 = 0 + 16n2
Combine like terms: -16n2 + 16n2 = 0
49m2 + 0 = 0 + 16n2
49m2 = 0 + 16n2
Remove the zero:
49m2 = 16n2
Divide each side by '49'.
m2 = 0.3265306122n2
Simplifying
m2 = 0.3265306122n2
Take the square root of each side:
m = {-0.571428571n, 0.571428571n}
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