2n^2=-3n-1

Solution for 2n^2=-3n-1 equation:

Simplifying
2n2 = -3n + -1

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

Solving
2n2 = -1 + -3n

Solving for variable 'n'.

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

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

Combine like terms: -1 + 1 = 0
1 + 3n + 2n2 = 0 + -3n + 3n
1 + 3n + 2n2 = -3n + 3n

Combine like terms: -3n + 3n = 0
1 + 3n + 2n2 = 0

Factor a trinomial.
(1 + n)(1 + 2n) = 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 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 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 + 2n = 0 + -1

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

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

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {-1, -0.5}