8n^2+4n-13=-n^2

Solution for 8n^2+4n-13=-n^2 equation:

Simplifying
8n2 + 4n + -13 = -1n2

Reorder the terms:
-13 + 4n + 8n2 = -1n2

Solving
-13 + 4n + 8n2 = -1n2

Solving for variable 'n'.

Combine like terms: 8n2 + n2 = 9n2
-13 + 4n + 9n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-13 + 4n + 9n2 = 0

Factor a trinomial.
(-13 + -9n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -9n)' equal to zero and attempt to solve:

Simplifying
-13 + -9n = 0

Solving
-13 + -9n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -9n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -9n = 0 + 13
-9n = 0 + 13

Combine like terms: 0 + 13 = 13
-9n = 13

Divide each side by '-9'.
n = -1.444444444

Simplifying
n = -1.444444444
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 = {-1.444444444, 1}