5n^2+41n+5=-3

Solution for 5n^2+41n+5=-3 equation:

Simplifying
5n2 + 41n + 5 = -3

Reorder the terms:
5 + 41n + 5n2 = -3

Solving
5 + 41n + 5n2 = -3

Solving for variable 'n'.

Reorder the terms:
5 + 3 + 41n + 5n2 = -3 + 3

Combine like terms: 5 + 3 = 8
8 + 41n + 5n2 = -3 + 3

Combine like terms: -3 + 3 = 0
8 + 41n + 5n2 = 0

Factor a trinomial.
(8 + n)(1 + 5n) = 0

Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5n = 0 + -1
5n = 0 + -1

Combine like terms: 0 + -1 = -1
5n = -1

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-8, -0.2}