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Simplifying
(4s + 5g)(4s + -5g) = 0
Reorder the terms:
(5g + 4s)(4s + -5g) = 0
Reorder the terms:
(5g + 4s)(-5g + 4s) = 0
Multiply (5g + 4s) * (-5g + 4s)
(5g * (-5g + 4s) + 4s * (-5g + 4s)) = 0
((-5g * 5g + 4s * 5g) + 4s * (-5g + 4s)) = 0
Reorder the terms:
((20gs + -25g2) + 4s * (-5g + 4s)) = 0
((20gs + -25g2) + 4s * (-5g + 4s)) = 0
(20gs + -25g2 + (-5g * 4s + 4s * 4s)) = 0
(20gs + -25g2 + (-20gs + 16s2)) = 0
Reorder the terms:
(20gs + -20gs + -25g2 + 16s2) = 0
Combine like terms: 20gs + -20gs = 0
(0 + -25g2 + 16s2) = 0
(-25g2 + 16s2) = 0
Solving
-25g2 + 16s2 = 0
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Add '-16s2' to each side of the equation.
-25g2 + 16s2 + -16s2 = 0 + -16s2
Combine like terms: 16s2 + -16s2 = 0
-25g2 + 0 = 0 + -16s2
-25g2 = 0 + -16s2
Remove the zero:
-25g2 = -16s2
Divide each side by '-25'.
g2 = 0.64s2
Simplifying
g2 = 0.64s2
Take the square root of each side:
g = {-0.8s, 0.8s}
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