2n^2=2-3n

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

Simplifying
2n2 = 2 + -3n

Solving
2n2 = 2 + -3n

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
(-2 + -1n)(1 + -2n) = 0

Subproblem 1
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
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 = {-2, 0.5}