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Simplifying
(8u + 9w)(8u + -9w) = 0
Multiply (8u + 9w) * (8u + -9w)
(8u * (8u + -9w) + 9w * (8u + -9w)) = 0
((8u * 8u + -9w * 8u) + 9w * (8u + -9w)) = 0
Reorder the terms:
((-72uw + 64u2) + 9w * (8u + -9w)) = 0
((-72uw + 64u2) + 9w * (8u + -9w)) = 0
(-72uw + 64u2 + (8u * 9w + -9w * 9w)) = 0
(-72uw + 64u2 + (72uw + -81w2)) = 0
Reorder the terms:
(-72uw + 72uw + 64u2 + -81w2) = 0
Combine like terms: -72uw + 72uw = 0
(0 + 64u2 + -81w2) = 0
(64u2 + -81w2) = 0
Solving
64u2 + -81w2 = 0
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Add '81w2' to each side of the equation.
64u2 + -81w2 + 81w2 = 0 + 81w2
Combine like terms: -81w2 + 81w2 = 0
64u2 + 0 = 0 + 81w2
64u2 = 0 + 81w2
Remove the zero:
64u2 = 81w2
Divide each side by '64'.
u2 = 1.265625w2
Simplifying
u2 = 1.265625w2
Take the square root of each side:
u = {-1.125w, 1.125w}
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