n^2-5n+6=20

Solution for n^2-5n+6=20 equation:

Simplifying
n2 + -5n + 6 = 20

Reorder the terms:
6 + -5n + n2 = 20

Solving
6 + -5n + n2 = 20

Solving for variable 'n'.

Reorder the terms:
6 + -20 + -5n + n2 = 20 + -20

Combine like terms: 6 + -20 = -14
-14 + -5n + n2 = 20 + -20

Combine like terms: 20 + -20 = 0
-14 + -5n + n2 = 0

Factor a trinomial.
(-2 + -1n)(7 + -1n) = 0

Subproblem 1
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
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 = {-2, 7}