2n^2-n+4=3n+2

Solution for 2n^2-n+4=3n+2 equation:

Simplifying
2n2 + -1n + 4 = 3n + 2

Reorder the terms:
4 + -1n + 2n2 = 3n + 2

Reorder the terms:
4 + -1n + 2n2 = 2 + 3n

Solving
4 + -1n + 2n2 = 2 + 3n

Solving for variable 'n'.

Reorder the terms:
4 + -2 + -1n + -3n + 2n2 = 2 + 3n + -2 + -3n

Combine like terms: 4 + -2 = 2
2 + -1n + -3n + 2n2 = 2 + 3n + -2 + -3n

Combine like terms: -1n + -3n = -4n
2 + -4n + 2n2 = 2 + 3n + -2 + -3n

Reorder the terms:
2 + -4n + 2n2 = 2 + -2 + 3n + -3n

Combine like terms: 2 + -2 = 0
2 + -4n + 2n2 = 0 + 3n + -3n
2 + -4n + 2n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
2 + -4n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2n + n2) = 0

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

Ignore the factor 2.
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 + -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, 1}