5n^2-38n+41=-7

Solution for 5n^2-38n+41=-7 equation:

Simplifying
5n2 + -38n + 41 = -7

Reorder the terms:
41 + -38n + 5n2 = -7

Solving
41 + -38n + 5n2 = -7

Solving for variable 'n'.

Reorder the terms:
41 + 7 + -38n + 5n2 = -7 + 7

Combine like terms: 41 + 7 = 48
48 + -38n + 5n2 = -7 + 7

Combine like terms: -7 + 7 = 0
48 + -38n + 5n2 = 0

Factor a trinomial.
(8 + -5n)(6 + -1n) = 0

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

Simplifying
8 + -5n = 0

Solving
8 + -5n = 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 + -5n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5n = 0 + -8
-5n = 0 + -8

Combine like terms: 0 + -8 = -8
-5n = -8

Divide each side by '-5'.
n = 1.6

Simplifying
n = 1.6
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {1.6, 6}