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Simplifying
(5v + 4g)(5v + -4g) = 0
Reorder the terms:
(4g + 5v)(5v + -4g) = 0
Reorder the terms:
(4g + 5v)(-4g + 5v) = 0
Multiply (4g + 5v) * (-4g + 5v)
(4g * (-4g + 5v) + 5v * (-4g + 5v)) = 0
((-4g * 4g + 5v * 4g) + 5v * (-4g + 5v)) = 0
Reorder the terms:
((20gv + -16g2) + 5v * (-4g + 5v)) = 0
((20gv + -16g2) + 5v * (-4g + 5v)) = 0
(20gv + -16g2 + (-4g * 5v + 5v * 5v)) = 0
(20gv + -16g2 + (-20gv + 25v2)) = 0
Reorder the terms:
(20gv + -20gv + -16g2 + 25v2) = 0
Combine like terms: 20gv + -20gv = 0
(0 + -16g2 + 25v2) = 0
(-16g2 + 25v2) = 0
Solving
-16g2 + 25v2 = 0
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Add '-25v2' to each side of the equation.
-16g2 + 25v2 + -25v2 = 0 + -25v2
Combine like terms: 25v2 + -25v2 = 0
-16g2 + 0 = 0 + -25v2
-16g2 = 0 + -25v2
Remove the zero:
-16g2 = -25v2
Divide each side by '-16'.
g2 = 1.5625v2
Simplifying
g2 = 1.5625v2
Take the square root of each side:
g = {-1.25v, 1.25v}
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