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

Solution for (3+u)(4u-1)=0 equation:

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

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

Multiply (3 + u) * (-1 + 4u)
(3(-1 + 4u) + u(-1 + 4u)) = 0
((-1 * 3 + 4u * 3) + u(-1 + 4u)) = 0
((-3 + 12u) + u(-1 + 4u)) = 0
(-3 + 12u + (-1 * u + 4u * u)) = 0
(-3 + 12u + (-1u + 4u2)) = 0

Combine like terms: 12u + -1u = 11u
(-3 + 11u + 4u2) = 0

Solving
-3 + 11u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(1 + -4u) = 0

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

Simplifying
-3 + -1u = 0

Solving
-3 + -1u = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1u = 0 + 3
-1u = 0 + 3

Combine like terms: 0 + 3 = 3
-1u = 3

Divide each side by '-1'.
u = -3

Simplifying
u = -3
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 = {-3, 0.25}