3n^2+n-41=-11

Solution for 3n^2+n-41=-11 equation:

Simplifying
3n2 + n + -41 = -11

Reorder the terms:
-41 + n + 3n2 = -11

Solving
-41 + n + 3n2 = -11

Solving for variable 'n'.

Reorder the terms:
-41 + 11 + n + 3n2 = -11 + 11

Combine like terms: -41 + 11 = -30
-30 + n + 3n2 = -11 + 11

Combine like terms: -11 + 11 = 0
-30 + n + 3n2 = 0

Factor a trinomial.
(-10 + -3n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-10 + -3n)' equal to zero and attempt to solve:

Simplifying
-10 + -3n = 0

Solving
-10 + -3n = 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 + -3n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3n = 0 + 10
-3n = 0 + 10

Combine like terms: 0 + 10 = 10
-3n = 10

Divide each side by '-3'.
n = -3.333333333

Simplifying
n = -3.333333333
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

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

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

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

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

Simplifying
n = 3
Solution
n = {-3.333333333, 3}