n^2-6n+3=-n^2-1

Solution for n^2-6n+3=-n^2-1 equation:

Simplifying
n2 + -6n + 3 = -1n2 + -1

Reorder the terms:
3 + -6n + n2 = -1n2 + -1

Reorder the terms:
3 + -6n + n2 = -1 + -1n2

Solving
3 + -6n + n2 = -1 + -1n2

Solving for variable 'n'.

Reorder the terms:
3 + 1 + -6n + n2 + n2 = -1 + -1n2 + 1 + n2

Combine like terms: 3 + 1 = 4
4 + -6n + n2 + n2 = -1 + -1n2 + 1 + n2

Combine like terms: n2 + n2 = 2n2
4 + -6n + 2n2 = -1 + -1n2 + 1 + n2

Reorder the terms:
4 + -6n + 2n2 = -1 + 1 + -1n2 + n2

Combine like terms: -1 + 1 = 0
4 + -6n + 2n2 = 0 + -1n2 + n2
4 + -6n + 2n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
4 + -6n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -3n + n2) = 0

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

Ignore the factor 2.
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 '(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
Solution
n = {1, 2}