2n^2=13n+n^2-42

Solution for 2n^2=13n+n^2-42 equation:

Simplifying
2n2 = 13n + n2 + -42

Reorder the terms:
2n2 = -42 + 13n + n2

Solving
2n2 = -42 + 13n + n2

Solving for variable 'n'.

Reorder the terms:
42 + -13n + 2n2 + -1n2 = -42 + 13n + n2 + 42 + -13n + -1n2

Combine like terms: 2n2 + -1n2 = 1n2
42 + -13n + 1n2 = -42 + 13n + n2 + 42 + -13n + -1n2

Reorder the terms:
42 + -13n + 1n2 = -42 + 42 + 13n + -13n + n2 + -1n2

Combine like terms: -42 + 42 = 0
42 + -13n + 1n2 = 0 + 13n + -13n + n2 + -1n2
42 + -13n + 1n2 = 13n + -13n + n2 + -1n2

Combine like terms: 13n + -13n = 0
42 + -13n + 1n2 = 0 + n2 + -1n2
42 + -13n + 1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
42 + -13n + 1n2 = 0

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

Subproblem 1
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
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 = {6, 7}