(3z-u)(6z+5u)=

Solution for (3z-u)(6z+5u)= equation:

Simplifying
(3z + -1u)(6z + 5u) = 0

Reorder the terms:
(-1u + 3z)(6z + 5u) = 0

Reorder the terms:
(-1u + 3z)(5u + 6z) = 0

Multiply (-1u + 3z) * (5u + 6z)
(-1u * (5u + 6z) + 3z * (5u + 6z)) = 0
((5u * -1u + 6z * -1u) + 3z * (5u + 6z)) = 0

Reorder the terms:
((-6uz + -5u2) + 3z * (5u + 6z)) = 0
((-6uz + -5u2) + 3z * (5u + 6z)) = 0
(-6uz + -5u2 + (5u * 3z + 6z * 3z)) = 0
(-6uz + -5u2 + (15uz + 18z2)) = 0

Reorder the terms:
(-6uz + 15uz + -5u2 + 18z2) = 0

Combine like terms: -6uz + 15uz = 9uz
(9uz + -5u2 + 18z2) = 0

Solving
9uz + -5u2 + 18z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5u + -6z)(u + -3z) = 0

Subproblem 1
Set the factor '(-5u + -6z)' equal to zero and attempt to solve:

Simplifying
-5u + -6z = 0

Solving
-5u + -6z = 0

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

Add '6z' to each side of the equation.
-5u + -6z + 6z = 0 + 6z

Combine like terms: -6z + 6z = 0
-5u + 0 = 0 + 6z
-5u = 0 + 6z
Remove the zero:
-5u = 6z

Divide each side by '-5'.
u = -1.2z

Simplifying
u = -1.2z
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 = {-1.2z, 3z}