2n*2n+4n-6=0

Solution for 2n*2n+4n-6=0 equation:

Simplifying
2n * 2n + 4n + -6 = 0

Reorder the terms for easier multiplication:
2 * 2n * n + 4n + -6 = 0

Multiply 2 * 2
4n * n + 4n + -6 = 0

Multiply n * n
4n2 + 4n + -6 = 0

Reorder the terms:
-6 + 4n + 4n2 = 0

Solving
-6 + 4n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2n + 2n2)' equal to zero and attempt to solve:

Simplifying
-3 + 2n + 2n2 = 0

Solving
-3 + 2n + 2n2 = 0

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

Divide each side by '2'.
-1.5 + n + n2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + n + 1.5 + n2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + n + n2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n + n2 = 0 + 1.5
n + n2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
n + n2 = 1.5

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 = 1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
1.25 + n2 = 1.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(n + 0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
n + 0.5 = 1.322875656

Simplifying
n + 0.5 = 1.322875656

Reorder the terms:
0.5 + n = 1.322875656

Solving
0.5 + n = 1.322875656

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 = 1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 1.322875656 + -0.5
n = 1.322875656 + -0.5

Combine like terms: 1.322875656 + -0.5 = 0.822875656
n = 0.822875656

Simplifying
n = 0.822875656

Subproblem 2
n + 0.5 = -1.322875656

Simplifying
n + 0.5 = -1.322875656

Reorder the terms:
0.5 + n = -1.322875656

Solving
0.5 + n = -1.322875656

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 = -1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -1.322875656 + -0.5
n = -1.322875656 + -0.5

Combine like terms: -1.322875656 + -0.5 = -1.822875656
n = -1.822875656

Simplifying
n = -1.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.822875656, -1.822875656}
Solution
n = {0.822875656, -1.822875656}