4n^2+6=8n

Solution for 4n^2+6=8n equation:

Simplifying
4n2 + 6 = 8n

Reorder the terms:
6 + 4n2 = 8n

Solving
6 + 4n2 = 8n

Solving for variable 'n'.

Reorder the terms:
6 + -8n + 4n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
6 + -8n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -4n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -4n + 2n2)' equal to zero and attempt to solve:

Simplifying
3 + -4n + 2n2 = 0

Solving
3 + -4n + 2n2 = 0

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

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

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -2n + -1.5 + n2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -2n + n2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -2n + n2 = 0 + -1.5
-2n + n2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-2n + n2 = -1.5

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 = -1.5 + 1

Reorder the terms:
1 + -2n + n2 = -1.5 + 1

Combine like terms: -1.5 + 1 = -0.5
1 + -2n + n2 = -0.5

Factor a perfect square on the left side:
(n + -1)(n + -1) = -0.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.