(4u+u)(4u+1)=0

Solution for (4u+u)(4u+1)=0 equation:

Simplifying
(4u + u)(4u + 1) = 0

Combine like terms: 4u + u = 5u
(5u)(4u + 1) = 0

Remove parenthesis around (5u)
5u(4u + 1) = 0

Reorder the terms:
5u(1 + 4u) = 0
(1 * 5u + 4u * 5u) = 0
(5u + 20u2) = 0

Solving
5u + 20u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5u'.
5u(1 + 4u) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(1 + 4u)' equal to zero and attempt to solve:

Simplifying
1 + 4u = 0

Solving
1 + 4u = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4u = 0 + -1
4u = 0 + -1

Combine like terms: 0 + -1 = -1
4u = -1

Divide each side by '4'.
u = -0.25

Simplifying
u = -0.25
Solution
u = {0, -0.25}