-n^2+2n+3=4

Solution for -n^2+2n+3=4 equation:

Simplifying
-1n2 + 2n + 3 = 4

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

Solving
3 + 2n + -1n2 = 4

Solving for variable 'n'.

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

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

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

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

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

Simplifying
-1 + n = 0

Solving
-1 + n = 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 + n = 0 + 1

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

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

Simplifying
n = 1
Subproblem 2
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
Solution
n = {1, 1}