(5.3n^2-6n+1.8)+(2n^2+3.8n-3.4)=

Solution for (5.3n^2-6n+1.8)+(2n^2+3.8n-3.4)= equation:

Simplifying
(5.3n2 + -6n + 1.8) + (2n2 + 3.8n + -3.4) = 0

Reorder the terms:
(1.8 + -6n + 5.3n2) + (2n2 + 3.8n + -3.4) = 0

Remove parenthesis around (1.8 + -6n + 5.3n2)
1.8 + -6n + 5.3n2 + (2n2 + 3.8n + -3.4) = 0

Reorder the terms:
1.8 + -6n + 5.3n2 + (-3.4 + 3.8n + 2n2) = 0

Remove parenthesis around (-3.4 + 3.8n + 2n2)
1.8 + -6n + 5.3n2 + -3.4 + 3.8n + 2n2 = 0

Reorder the terms:
1.8 + -3.4 + -6n + 3.8n + 5.3n2 + 2n2 = 0

Combine like terms: 1.8 + -3.4 = -1.6
-1.6 + -6n + 3.8n + 5.3n2 + 2n2 = 0

Combine like terms: -6n + 3.8n = -2.2n
-1.6 + -2.2n + 5.3n2 + 2n2 = 0

Combine like terms: 5.3n2 + 2n2 = 7.3n2
-1.6 + -2.2n + 7.3n2 = 0

Solving
-1.6 + -2.2n + 7.3n2 = 0

Solving for variable 'n'.

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

Divide each side by '7.3'.
-0.2191780822 + -0.301369863n + n2 = 0

Move the constant term to the right:

Add '0.2191780822' to each side of the equation.
-0.2191780822 + -0.301369863n + 0.2191780822 + n2 = 0 + 0.2191780822

Reorder the terms:
-0.2191780822 + 0.2191780822 + -0.301369863n + n2 = 0 + 0.2191780822

Combine like terms: -0.2191780822 + 0.2191780822 = 0.0000000000
0.0000000000 + -0.301369863n + n2 = 0 + 0.2191780822
-0.301369863n + n2 = 0 + 0.2191780822

Combine like terms: 0 + 0.2191780822 = 0.2191780822
-0.301369863n + n2 = 0.2191780822

The n term is -0.301369863n.  Take half its coefficient (-0.1506849315).
Square it (0.02270594858) and add it to both sides.

Add '0.02270594858' to each side of the equation.
-0.301369863n + 0.02270594858 + n2 = 0.2191780822 + 0.02270594858

Reorder the terms:
0.02270594858 + -0.301369863n + n2 = 0.2191780822 + 0.02270594858

Combine like terms: 0.2191780822 + 0.02270594858 = 0.24188403078
0.02270594858 + -0.301369863n + n2 = 0.24188403078

Factor a perfect square on the left side:
(n + -0.1506849315)(n + -0.1506849315) = 0.24188403078

Calculate the square root of the right side: 0.49181707

Break this problem into two subproblems by setting 
(n + -0.1506849315) equal to 0.49181707 and -0.49181707.

Subproblem 1
n + -0.1506849315 = 0.49181707

Simplifying
n + -0.1506849315 = 0.49181707

Reorder the terms:
-0.1506849315 + n = 0.49181707

Solving
-0.1506849315 + n = 0.49181707

Solving for variable 'n'.

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

Add '0.1506849315' to each side of the equation.
-0.1506849315 + 0.1506849315 + n = 0.49181707 + 0.1506849315

Combine like terms: -0.1506849315 + 0.1506849315 = 0.0000000000
0.0000000000 + n = 0.49181707 + 0.1506849315
n = 0.49181707 + 0.1506849315

Combine like terms: 0.49181707 + 0.1506849315 = 0.6425020015
n = 0.6425020015

Simplifying
n = 0.6425020015

Subproblem 2
n + -0.1506849315 = -0.49181707

Simplifying
n + -0.1506849315 = -0.49181707

Reorder the terms:
-0.1506849315 + n = -0.49181707

Solving
-0.1506849315 + n = -0.49181707

Solving for variable 'n'.

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

Add '0.1506849315' to each side of the equation.
-0.1506849315 + 0.1506849315 + n = -0.49181707 + 0.1506849315

Combine like terms: -0.1506849315 + 0.1506849315 = 0.0000000000
0.0000000000 + n = -0.49181707 + 0.1506849315
n = -0.49181707 + 0.1506849315

Combine like terms: -0.49181707 + 0.1506849315 = -0.3411321385
n = -0.3411321385

Simplifying
n = -0.3411321385

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.6425020015, -0.3411321385}