3n^2+34n+40=0

Solution for 3n^2+34n+40=0 equation:

Simplifying
3n2 + 34n + 40 = 0

Reorder the terms:
40 + 34n + 3n2 = 0

Solving
40 + 34n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(10 + n)(4 + 3n) = 0

Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve:

Simplifying
10 + n = 0

Solving
10 + n = 0

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

Add '-10' to each side of the equation.
10 + -10 + n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + n = 0 + -10
n = 0 + -10

Combine like terms: 0 + -10 = -10
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(4 + 3n)' equal to zero and attempt to solve:

Simplifying
4 + 3n = 0

Solving
4 + 3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3n = 0 + -4
3n = 0 + -4

Combine like terms: 0 + -4 = -4
3n = -4

Divide each side by '3'.
n = -1.333333333

Simplifying
n = -1.333333333
Solution
n = {-10, -1.333333333}