n^2+2n-1=7

Solution for n^2+2n-1=7 equation:

Simplifying
n2 + 2n + -1 = 7

Reorder the terms:
-1 + 2n + n2 = 7

Solving
-1 + 2n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
-1 + -7 + 2n + n2 = 7 + -7

Combine like terms: -1 + -7 = -8
-8 + 2n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-8 + 2n + n2 = 0

Factor a trinomial.
(-4 + -1n)(2 + -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 '(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 = {-4, 2}