5n^2+1=-6n

Solution for 5n^2+1=-6n equation:

Simplifying
5n2 + 1 = -6n

Reorder the terms:
1 + 5n2 = -6n

Solving
1 + 5n2 = -6n

Solving for variable 'n'.

Reorder the terms:
1 + 6n + 5n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
1 + 6n + 5n2 = 0

Factor a trinomial.
(1 + n)(1 + 5n) = 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 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 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 + 5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5n = 0 + -1
5n = 0 + -1

Combine like terms: 0 + -1 = -1
5n = -1

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-1, -0.2}