n^2-7n+4=-6

Solution for n^2-7n+4=-6 equation:

Simplifying
n2 + -7n + 4 = -6

Reorder the terms:
4 + -7n + n2 = -6

Solving
4 + -7n + n2 = -6

Solving for variable 'n'.

Reorder the terms:
4 + 6 + -7n + n2 = -6 + 6

Combine like terms: 4 + 6 = 10
10 + -7n + n2 = -6 + 6

Combine like terms: -6 + 6 = 0
10 + -7n + n2 = 0

Factor a trinomial.
(2 + -1n)(5 + -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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {2, 5}