n^2=42-11n

Solution for n^2=42-11n equation:

Simplifying
n2 = 42 + -11n

Solving
n2 = 42 + -11n

Solving for variable 'n'.

Reorder the terms:
-42 + 11n + n2 = 42 + -11n + -42 + 11n

Reorder the terms:
-42 + 11n + n2 = 42 + -42 + -11n + 11n

Combine like terms: 42 + -42 = 0
-42 + 11n + n2 = 0 + -11n + 11n
-42 + 11n + n2 = -11n + 11n

Combine like terms: -11n + 11n = 0
-42 + 11n + n2 = 0

Factor a trinomial.
(-14 + -1n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-14 + -1n)' equal to zero and attempt to solve:

Simplifying
-14 + -1n = 0

Solving
-14 + -1n = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1n = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1n = 0 + 14
-1n = 0 + 14

Combine like terms: 0 + 14 = 14
-1n = 14

Divide each side by '-1'.
n = -14

Simplifying
n = -14
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 = {-14, 3}