(3z-u)*(2z+3u)=0

Solution for (3z-u)*(2z+3u)=0 equation:

Simplifying
(3z + -1u)(2z + 3u) = 0

Reorder the terms:
(-1u + 3z)(2z + 3u) = 0

Reorder the terms:
(-1u + 3z)(3u + 2z) = 0

Multiply (-1u + 3z) * (3u + 2z)
(-1u * (3u + 2z) + 3z * (3u + 2z)) = 0
((3u * -1u + 2z * -1u) + 3z * (3u + 2z)) = 0

Reorder the terms:
((-2uz + -3u2) + 3z * (3u + 2z)) = 0
((-2uz + -3u2) + 3z * (3u + 2z)) = 0
(-2uz + -3u2 + (3u * 3z + 2z * 3z)) = 0
(-2uz + -3u2 + (9uz + 6z2)) = 0

Reorder the terms:
(-2uz + 9uz + -3u2 + 6z2) = 0

Combine like terms: -2uz + 9uz = 7uz
(7uz + -3u2 + 6z2) = 0

Solving
7uz + -3u2 + 6z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3u + -2z)(u + -3z) = 0

Subproblem 1
Set the factor '(-3u + -2z)' equal to zero and attempt to solve:

Simplifying
-3u + -2z = 0

Solving
-3u + -2z = 0

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

Add '2z' to each side of the equation.
-3u + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
-3u + 0 = 0 + 2z
-3u = 0 + 2z
Remove the zero:
-3u = 2z

Divide each side by '-3'.
u = -0.6666666667z

Simplifying
u = -0.6666666667z
Subproblem 2
Set the factor '(u + -3z)' equal to zero and attempt to solve:

Simplifying
u + -3z = 0

Solving
u + -3z = 0

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

Add '3z' to each side of the equation.
u + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
u + 0 = 0 + 3z
u = 0 + 3z
Remove the zero:
u = 3z

Simplifying
u = 3z
Solution
u = {-0.6666666667z, 3z}