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Simplifying
(5v + 7w)(5v + -7w) = 0
Multiply (5v + 7w) * (5v + -7w)
(5v * (5v + -7w) + 7w * (5v + -7w)) = 0
((5v * 5v + -7w * 5v) + 7w * (5v + -7w)) = 0
Reorder the terms:
((-35vw + 25v2) + 7w * (5v + -7w)) = 0
((-35vw + 25v2) + 7w * (5v + -7w)) = 0
(-35vw + 25v2 + (5v * 7w + -7w * 7w)) = 0
(-35vw + 25v2 + (35vw + -49w2)) = 0
Reorder the terms:
(-35vw + 35vw + 25v2 + -49w2) = 0
Combine like terms: -35vw + 35vw = 0
(0 + 25v2 + -49w2) = 0
(25v2 + -49w2) = 0
Solving
25v2 + -49w2 = 0
Solving for variable 'v'.
Move all terms containing v to the left, all other terms to the right.
Add '49w2' to each side of the equation.
25v2 + -49w2 + 49w2 = 0 + 49w2
Combine like terms: -49w2 + 49w2 = 0
25v2 + 0 = 0 + 49w2
25v2 = 0 + 49w2
Remove the zero:
25v2 = 49w2
Divide each side by '25'.
v2 = 1.96w2
Simplifying
v2 = 1.96w2
Take the square root of each side:
v = {-1.4w, 1.4w}
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