N^2+3N-1=3

Solution for N^2+3N-1=3 equation:

Simplifying
N2 + 3N + -1 = 3

Reorder the terms:
-1 + 3N + N2 = 3

Solving
-1 + 3N + N2 = 3

Solving for variable 'N'.

Reorder the terms:
-1 + -3 + 3N + N2 = 3 + -3

Combine like terms: -1 + -3 = -4
-4 + 3N + N2 = 3 + -3

Combine like terms: 3 + -3 = 0
-4 + 3N + N2 = 0

Factor a trinomial.
(-4 + -1N)(1 + -1N) = 0

Subproblem 1
Set the factor '(-4 + -1N)' equal to zero and attempt to solve:

Simplifying
-4 + -1N = 0

Solving
-4 + -1N = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1N = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1N = 0 + 4
-1N = 0 + 4

Combine like terms: 0 + 4 = 4
-1N = 4

Divide each side by '-1'.
N = -4

Simplifying
N = -4
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 = {-4, 1}