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

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


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

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

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

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

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

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

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

Solving
6uz + -3u2 + 9z2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2uz + -1u2 + 3z2) = 0

Factor a trinomial.
3((-1u + -1z)(u + -3z)) = 0

Ignore the factor 3.

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

Simplifying
-1u + -1z = 0

Solving
-1u + -1z = 0

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

Add 'z' to each side of the equation.
-1u + -1z + z = 0 + z

Combine like terms: -1z + z = 0
-1u + 0 = 0 + z
-1u = 0 + z
Remove the zero:
-1u = z

Divide each side by '-1'.
u = -1z

Simplifying
u = -1z

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 = {-1z, 3z}

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