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Simplifying
(3y + 4z)(3y + -4z) = 0
Multiply (3y + 4z) * (3y + -4z)
(3y * (3y + -4z) + 4z * (3y + -4z)) = 0
((3y * 3y + -4z * 3y) + 4z * (3y + -4z)) = 0
Reorder the terms:
((-12yz + 9y2) + 4z * (3y + -4z)) = 0
((-12yz + 9y2) + 4z * (3y + -4z)) = 0
(-12yz + 9y2 + (3y * 4z + -4z * 4z)) = 0
(-12yz + 9y2 + (12yz + -16z2)) = 0
Reorder the terms:
(-12yz + 12yz + 9y2 + -16z2) = 0
Combine like terms: -12yz + 12yz = 0
(0 + 9y2 + -16z2) = 0
(9y2 + -16z2) = 0
Solving
9y2 + -16z2 = 0
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '16z2' to each side of the equation.
9y2 + -16z2 + 16z2 = 0 + 16z2
Combine like terms: -16z2 + 16z2 = 0
9y2 + 0 = 0 + 16z2
9y2 = 0 + 16z2
Remove the zero:
9y2 = 16z2
Divide each side by '9'.
y2 = 1.777777778z2
Simplifying
y2 = 1.777777778z2
Take the square root of each side:
y = {-1.333333333z, 1.333333333z}
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