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

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

Simplifying
(2n2 + n + -4) + -1(n2 + 3n + 2) = 0

Reorder the terms:
(-4 + n + 2n2) + -1(n2 + 3n + 2) = 0

Remove parenthesis around (-4 + n + 2n2)
-4 + n + 2n2 + -1(n2 + 3n + 2) = 0

Reorder the terms:
-4 + n + 2n2 + -1(2 + 3n + n2) = 0
-4 + n + 2n2 + (2 * -1 + 3n * -1 + n2 * -1) = 0
-4 + n + 2n2 + (-2 + -3n + -1n2) = 0

Reorder the terms:
-4 + -2 + n + -3n + 2n2 + -1n2 = 0

Combine like terms: -4 + -2 = -6
-6 + n + -3n + 2n2 + -1n2 = 0

Combine like terms: n + -3n = -2n
-6 + -2n + 2n2 + -1n2 = 0

Combine like terms: 2n2 + -1n2 = 1n2
-6 + -2n + 1n2 = 0

Solving
-6 + -2n + 1n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + -2n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2n + n2 = 0 + 6
-2n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2n + n2 = 6

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 6 + 1

Reorder the terms:
1 + -2n + n2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2n + n2 = 7

Factor a perfect square on the left side:
(n + -1)(n + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
n + -1 = 2.645751311

Simplifying
n + -1 = 2.645751311

Reorder the terms:
-1 + n = 2.645751311

Solving
-1 + n = 2.645751311

Solving for variable 'n'.

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 = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + n = 2.645751311 + 1
n = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
n = 3.645751311

Simplifying
n = 3.645751311

Subproblem 2
n + -1 = -2.645751311

Simplifying
n + -1 = -2.645751311

Reorder the terms:
-1 + n = -2.645751311

Solving
-1 + n = -2.645751311

Solving for variable 'n'.

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 = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + n = -2.645751311 + 1
n = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
n = -1.645751311

Simplifying
n = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.645751311, -1.645751311}