5n^2=-42+41n

Solution for 5n^2=-42+41n equation:

Simplifying
5n2 = -42 + 41n

Solving
5n2 = -42 + 41n

Solving for variable 'n'.

Reorder the terms:
42 + -41n + 5n2 = -42 + 41n + 42 + -41n

Reorder the terms:
42 + -41n + 5n2 = -42 + 42 + 41n + -41n

Combine like terms: -42 + 42 = 0
42 + -41n + 5n2 = 0 + 41n + -41n
42 + -41n + 5n2 = 41n + -41n

Combine like terms: 41n + -41n = 0
42 + -41n + 5n2 = 0

Factor a trinomial.
(6 + -5n)(7 + -1n) = 0

Subproblem 1
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 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 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {1.2, 7}