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

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


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

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

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

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

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

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

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

Solving
3uz + -2u2 + 9z2 = 0

Solving for variable 'u'.

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


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

Simplifying
-2u + -3z = 0

Solving
-2u + -3z = 0

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

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

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

Divide each side by '-2'.
u = -1.5z

Simplifying
u = -1.5z

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 = {-1.5z, 3z}

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