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Simplifying
(3xy + 5z)(3xy + -5z) = 0
Multiply (3xy + 5z) * (3xy + -5z)
(3xy * (3xy + -5z) + 5z * (3xy + -5z)) = 0
((3xy * 3xy + -5z * 3xy) + 5z * (3xy + -5z)) = 0
Reorder the terms:
((-15xyz + 9x2y2) + 5z * (3xy + -5z)) = 0
((-15xyz + 9x2y2) + 5z * (3xy + -5z)) = 0
(-15xyz + 9x2y2 + (3xy * 5z + -5z * 5z)) = 0
(-15xyz + 9x2y2 + (15xyz + -25z2)) = 0
Reorder the terms:
(-15xyz + 15xyz + 9x2y2 + -25z2) = 0
Combine like terms: -15xyz + 15xyz = 0
(0 + 9x2y2 + -25z2) = 0
(9x2y2 + -25z2) = 0
Solving
9x2y2 + -25z2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25z2' to each side of the equation.
9x2y2 + -25z2 + 25z2 = 0 + 25z2
Combine like terms: -25z2 + 25z2 = 0
9x2y2 + 0 = 0 + 25z2
9x2y2 = 0 + 25z2
Remove the zero:
9x2y2 = 25z2
Divide each side by '9y2'.
x2 = 2.777777778y-2z2
Simplifying
x2 = 2.777777778y-2z2
Take the square root of each side:
x = {-1.666666667y-1z, 1.666666667y-1z}
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