n^2-5n+6=42

Solution for n^2-5n+6=42 equation:

Simplifying
n2 + -5n + 6 = 42

Reorder the terms:
6 + -5n + n2 = 42

Solving
6 + -5n + n2 = 42

Solving for variable 'n'.

Reorder the terms:
6 + -42 + -5n + n2 = 42 + -42

Combine like terms: 6 + -42 = -36
-36 + -5n + n2 = 42 + -42

Combine like terms: 42 + -42 = 0
-36 + -5n + n2 = 0

Factor a trinomial.
(-4 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {-4, 9}