-n^2-2n+1=4-2n^2

Solution for -n^2-2n+1=4-2n^2 equation:

Simplifying
-1n2 + -2n + 1 = 4 + -2n2

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

Solving
1 + -2n + -1n2 = 4 + -2n2

Solving for variable 'n'.

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

Combine like terms: 1 + -4 = -3
-3 + -2n + -1n2 + 2n2 = 4 + -2n2 + -4 + 2n2

Combine like terms: -1n2 + 2n2 = 1n2
-3 + -2n + 1n2 = 4 + -2n2 + -4 + 2n2

Reorder the terms:
-3 + -2n + 1n2 = 4 + -4 + -2n2 + 2n2

Combine like terms: 4 + -4 = 0
-3 + -2n + 1n2 = 0 + -2n2 + 2n2
-3 + -2n + 1n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-3 + -2n + 1n2 = 0

Factor a trinomial.
(-1 + -1n)(3 + -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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-1, 3}