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

Solution for (6+u)(4u+1)=0 equation:

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

Reorder the terms:
(6 + u)(1 + 4u) = 0

Multiply (6 + u) * (1 + 4u)
(6(1 + 4u) + u(1 + 4u)) = 0
((1 * 6 + 4u * 6) + u(1 + 4u)) = 0
((6 + 24u) + u(1 + 4u)) = 0
(6 + 24u + (1 * u + 4u * u)) = 0
(6 + 24u + (1u + 4u2)) = 0

Combine like terms: 24u + 1u = 25u
(6 + 25u + 4u2) = 0

Solving
6 + 25u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6 + u)(1 + 4u) = 0

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

Simplifying
6 + u = 0

Solving
6 + u = 0

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

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

Combine like terms: 6 + -6 = 0
0 + u = 0 + -6
u = 0 + -6

Combine like terms: 0 + -6 = -6
u = -6

Simplifying
u = -6
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 = {-6, -0.25}