(3z-u)(3z+4u)=

Solution for (3z-u)(3z+4u)= equation:

Simplifying
(3z + -1u)(3z + 4u) = 0

Reorder the terms:
(-1u + 3z)(3z + 4u) = 0

Reorder the terms:
(-1u + 3z)(4u + 3z) = 0

Multiply (-1u + 3z) * (4u + 3z)
(-1u * (4u + 3z) + 3z * (4u + 3z)) = 0
((4u * -1u + 3z * -1u) + 3z * (4u + 3z)) = 0

Reorder the terms:
((-3uz + -4u2) + 3z * (4u + 3z)) = 0
((-3uz + -4u2) + 3z * (4u + 3z)) = 0
(-3uz + -4u2 + (4u * 3z + 3z * 3z)) = 0
(-3uz + -4u2 + (12uz + 9z2)) = 0

Reorder the terms:
(-3uz + 12uz + -4u2 + 9z2) = 0

Combine like terms: -3uz + 12uz = 9uz
(9uz + -4u2 + 9z2) = 0

Solving
9uz + -4u2 + 9z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4u + -3z)(u + -3z) = 0

Subproblem 1
Set the factor '(-4u + -3z)' equal to zero and attempt to solve:

Simplifying
-4u + -3z = 0

Solving
-4u + -3z = 0

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

Add '3z' to each side of the equation.
-4u + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
-4u + 0 = 0 + 3z
-4u = 0 + 3z
Remove the zero:
-4u = 3z

Divide each side by '-4'.
u = -0.75z

Simplifying
u = -0.75z
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 = {-0.75z, 3z}