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

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


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

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

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

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

Reorder the terms:
((-6uz + -3u2) + 5z * (3u + 6z)) = 0
((-6uz + -3u2) + 5z * (3u + 6z)) = 0
(-6uz + -3u2 + (3u * 5z + 6z * 5z)) = 0
(-6uz + -3u2 + (15uz + 30z2)) = 0

Reorder the terms:
(-6uz + 15uz + -3u2 + 30z2) = 0

Combine like terms: -6uz + 15uz = 9uz
(9uz + -3u2 + 30z2) = 0

Solving
9uz + -3u2 + 30z2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3uz + -1u2 + 10z2) = 0

Factor a trinomial.
3((-1u + -2z)(u + -5z)) = 0

Ignore the factor 3.

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

Simplifying
-1u + -2z = 0

Solving
-1u + -2z = 0

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

Add '2z' to each side of the equation.
-1u + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
-1u + 0 = 0 + 2z
-1u = 0 + 2z
Remove the zero:
-1u = 2z

Divide each side by '-1'.
u = -2z

Simplifying
u = -2z

Subproblem 2
Set the factor '(u + -5z)' equal to zero and attempt to solve:

Simplifying
u + -5z = 0

Solving
u + -5z = 0

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

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

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

Simplifying
u = 5z
Solution
u = {-2z, 5z}

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