n^2-10n+7=-2

Solution for n^2-10n+7=-2 equation:

Simplifying
n2 + -10n + 7 = -2

Reorder the terms:
7 + -10n + n2 = -2

Solving
7 + -10n + n2 = -2

Solving for variable 'n'.

Reorder the terms:
7 + 2 + -10n + n2 = -2 + 2

Combine like terms: 7 + 2 = 9
9 + -10n + n2 = -2 + 2

Combine like terms: -2 + 2 = 0
9 + -10n + n2 = 0

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
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 = {1, 9}