y(3xy-4)(3xy+4)=0

Solution for y(3xy-4)(3xy+4)=0 equation:

Simplifying
y(3xy + -4)(3xy + 4) = 0

Reorder the terms:
y(-4 + 3xy)(3xy + 4) = 0

Reorder the terms:
y(-4 + 3xy)(4 + 3xy) = 0

Multiply (-4 + 3xy) * (4 + 3xy)
y(-4(4 + 3xy) + 3xy * (4 + 3xy)) = 0
y((4 * -4 + 3xy * -4) + 3xy * (4 + 3xy)) = 0
y((-16 + -12xy) + 3xy * (4 + 3xy)) = 0
y(-16 + -12xy + (4 * 3xy + 3xy * 3xy)) = 0
y(-16 + -12xy + (12xy + 9x2y2)) = 0

Combine like terms: -12xy + 12xy = 0
y(-16 + 0 + 9x2y2) = 0
y(-16 + 9x2y2) = 0
(-16 * y + 9x2y2 * y) = 0

Reorder the terms:
(9x2y3 + -16y) = 0
(9x2y3 + -16y) = 0

Solving
9x2y3 + -16y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '16y' to each side of the equation.
9x2y3 + -16y + 16y = 0 + 16y

Combine like terms: -16y + 16y = 0
9x2y3 + 0 = 0 + 16y
9x2y3 = 0 + 16y
Remove the zero:
9x2y3 = 16y

Divide each side by '9y3'.
x2 = 1.777777778y-2

Simplifying
x2 = 1.777777778y-2

Take the square root of each side:
x = {-1.333333333y-1, 1.333333333y-1}