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Simplifying
(9y + 5z)(9y + -5z) = 0
Multiply (9y + 5z) * (9y + -5z)
(9y * (9y + -5z) + 5z * (9y + -5z)) = 0
((9y * 9y + -5z * 9y) + 5z * (9y + -5z)) = 0
Reorder the terms:
((-45yz + 81y2) + 5z * (9y + -5z)) = 0
((-45yz + 81y2) + 5z * (9y + -5z)) = 0
(-45yz + 81y2 + (9y * 5z + -5z * 5z)) = 0
(-45yz + 81y2 + (45yz + -25z2)) = 0
Reorder the terms:
(-45yz + 45yz + 81y2 + -25z2) = 0
Combine like terms: -45yz + 45yz = 0
(0 + 81y2 + -25z2) = 0
(81y2 + -25z2) = 0
Solving
81y2 + -25z2 = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '25z2' to each side of the equation.
81y2 + -25z2 + 25z2 = 0 + 25z2
Combine like terms: -25z2 + 25z2 = 0
81y2 + 0 = 0 + 25z2
81y2 = 0 + 25z2
Remove the zero:
81y2 = 25z2
Divide each side by '81'.
y2 = 0.3086419753z2
Simplifying
y2 = 0.3086419753z2
Take the square root of each side:
y = {-0.555555556z, 0.555555556z}
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