n^2-12n+13=-7

Solution for n^2-12n+13=-7 equation:

Simplifying
n2 + -12n + 13 = -7

Reorder the terms:
13 + -12n + n2 = -7

Solving
13 + -12n + n2 = -7

Solving for variable 'n'.

Reorder the terms:
13 + 7 + -12n + n2 = -7 + 7

Combine like terms: 13 + 7 = 20
20 + -12n + n2 = -7 + 7

Combine like terms: -7 + 7 = 0
20 + -12n + n2 = 0

Factor a trinomial.
(2 + -1n)(10 + -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 '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {2, 10}