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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}
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