3u^2+40u+13=0

Solution for 3u^2+40u+13=0 equation:

Simplifying
3u2 + 40u + 13 = 0

Reorder the terms:
13 + 40u + 3u2 = 0

Solving
13 + 40u + 3u2 = 0

Solving for variable 'u'.

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

Subproblem 1
Set the factor '(13 + u)' equal to zero and attempt to solve:

Simplifying
13 + u = 0

Solving
13 + u = 0

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

Add '-13' to each side of the equation.
13 + -13 + u = 0 + -13

Combine like terms: 13 + -13 = 0
0 + u = 0 + -13
u = 0 + -13

Combine like terms: 0 + -13 = -13
u = -13

Simplifying
u = -13
Subproblem 2
Set the factor '(1 + 3u)' equal to zero and attempt to solve:

Simplifying
1 + 3u = 0

Solving
1 + 3u = 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 + 3u = 0 + -1

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

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

Divide each side by '3'.
u = -0.3333333333

Simplifying
u = -0.3333333333
Solution
u = {-13, -0.3333333333}