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Simplifying
(3w + 5g)(3w + -5g) = 0
Reorder the terms:
(5g + 3w)(3w + -5g) = 0
Reorder the terms:
(5g + 3w)(-5g + 3w) = 0
Multiply (5g + 3w) * (-5g + 3w)
(5g * (-5g + 3w) + 3w * (-5g + 3w)) = 0
((-5g * 5g + 3w * 5g) + 3w * (-5g + 3w)) = 0
Reorder the terms:
((15gw + -25g2) + 3w * (-5g + 3w)) = 0
((15gw + -25g2) + 3w * (-5g + 3w)) = 0
(15gw + -25g2 + (-5g * 3w + 3w * 3w)) = 0
(15gw + -25g2 + (-15gw + 9w2)) = 0
Reorder the terms:
(15gw + -15gw + -25g2 + 9w2) = 0
Combine like terms: 15gw + -15gw = 0
(0 + -25g2 + 9w2) = 0
(-25g2 + 9w2) = 0
Solving
-25g2 + 9w2 = 0
Solving for variable 'g'.
Move all terms containing g to the left, all other terms to the right.
Add '-9w2' to each side of the equation.
-25g2 + 9w2 + -9w2 = 0 + -9w2
Combine like terms: 9w2 + -9w2 = 0
-25g2 + 0 = 0 + -9w2
-25g2 = 0 + -9w2
Remove the zero:
-25g2 = -9w2
Divide each side by '-25'.
g2 = 0.36w2
Simplifying
g2 = 0.36w2
Take the square root of each side:
g = {-0.6w, 0.6w}
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