2n^2+n+2=3

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

Simplifying
2n2 + n + 2 = 3

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

Solving
2 + n + 2n2 = 3

Solving for variable 'n'.

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

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

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

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

Subproblem 1
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
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}