5n^2=42-11n

Solution for 5n^2=42-11n equation:

Simplifying
5n2 = 42 + -11n

Solving
5n2 = 42 + -11n

Solving for variable 'n'.

Reorder the terms:
-42 + 11n + 5n2 = 42 + -11n + -42 + 11n

Reorder the terms:
-42 + 11n + 5n2 = 42 + -42 + -11n + 11n

Combine like terms: 42 + -42 = 0
-42 + 11n + 5n2 = 0 + -11n + 11n
-42 + 11n + 5n2 = -11n + 11n

Combine like terms: -11n + 11n = 0
-42 + 11n + 5n2 = 0

Factor a trinomial.
(-21 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-21 + -5n)' equal to zero and attempt to solve:

Simplifying
-21 + -5n = 0

Solving
-21 + -5n = 0

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

Add '21' to each side of the equation.
-21 + 21 + -5n = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -5n = 0 + 21
-5n = 0 + 21

Combine like terms: 0 + 21 = 21
-5n = 21

Divide each side by '-5'.
n = -4.2

Simplifying
n = -4.2
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-4.2, 2}