(xy+3z)(xy-3z)=0

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

Simplifying
(xy + 3z)(xy + -3z) = 0

Multiply (xy + 3z) * (xy + -3z)
(xy(xy + -3z) + 3z * (xy + -3z)) = 0
((xy * xy + -3z * xy) + 3z * (xy + -3z)) = 0

Reorder the terms:
((-3xyz + x2y2) + 3z * (xy + -3z)) = 0
((-3xyz + x2y2) + 3z * (xy + -3z)) = 0
(-3xyz + x2y2 + (xy * 3z + -3z * 3z)) = 0
(-3xyz + x2y2 + (3xyz + -9z2)) = 0

Reorder the terms:
(-3xyz + 3xyz + x2y2 + -9z2) = 0

Combine like terms: -3xyz + 3xyz = 0
(0 + x2y2 + -9z2) = 0
(x2y2 + -9z2) = 0

Solving
x2y2 + -9z2 = 0

Solving for variable 'x'.

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

Add '9z2' to each side of the equation.
x2y2 + -9z2 + 9z2 = 0 + 9z2

Combine like terms: -9z2 + 9z2 = 0
x2y2 + 0 = 0 + 9z2
x2y2 = 0 + 9z2
Remove the zero:
x2y2 = 9z2

Divide each side by 'y2'.
x2 = 9y-2z2

Simplifying
x2 = 9y-2z2

Take the square root of each side:
x = {-3y-1z, 3y-1z}