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

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

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

Multiply (3 + n) * (4 + -2n)
(3(4 + -2n) + n(4 + -2n)) = -3
((4 * 3 + -2n * 3) + n(4 + -2n)) = -3
((12 + -6n) + n(4 + -2n)) = -3
(12 + -6n + (4 * n + -2n * n)) = -3
(12 + -6n + (4n + -2n2)) = -3

Combine like terms: -6n + 4n = -2n
(12 + -2n + -2n2) = -3

Solving
12 + -2n + -2n2 = -3

Solving for variable 'n'.

Reorder the terms:
12 + 3 + -2n + -2n2 = -3 + 3

Combine like terms: 12 + 3 = 15
15 + -2n + -2n2 = -3 + 3

Combine like terms: -3 + 3 = 0
15 + -2n + -2n2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-7.5 + n + n2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + n + 7.5 + n2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + n + n2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + n + n2 = 0 + 7.5
n + n2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
n + n2 = 7.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + n2 = 7.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 7.5 + 0.25

Combine like terms: 7.5 + 0.25 = 7.75
1.25 + n2 = 7.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 7.75

Calculate the square root of the right side: 2.783882181

Break this problem into two subproblems by setting 
(n + 0.5) equal to 2.783882181 and -2.783882181.

Subproblem 1
n + 0.5 = 2.783882181

Simplifying
n + 0.5 = 2.783882181

Reorder the terms:
0.5 + n = 2.783882181

Solving
0.5 + n = 2.783882181

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 2.783882181 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 2.783882181 + -0.5
n = 2.783882181 + -0.5

Combine like terms: 2.783882181 + -0.5 = 2.283882181
n = 2.283882181

Simplifying
n = 2.283882181

Subproblem 2
n + 0.5 = -2.783882181

Simplifying
n + 0.5 = -2.783882181

Reorder the terms:
0.5 + n = -2.783882181

Solving
0.5 + n = -2.783882181

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -2.783882181 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -2.783882181 + -0.5
n = -2.783882181 + -0.5

Combine like terms: -2.783882181 + -0.5 = -3.283882181
n = -3.283882181

Simplifying
n = -3.283882181

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.283882181, -3.283882181}