4n^2=64n-2

Solution for 4n^2=64n-2 equation:

Simplifying
4n2 = 64n + -2

Reorder the terms:
4n2 = -2 + 64n

Solving
4n2 = -2 + 64n

Solving for variable 'n'.

Reorder the terms:
2 + -64n + 4n2 = -2 + 64n + 2 + -64n

Reorder the terms:
2 + -64n + 4n2 = -2 + 2 + 64n + -64n

Combine like terms: -2 + 2 = 0
2 + -64n + 4n2 = 0 + 64n + -64n
2 + -64n + 4n2 = 64n + -64n

Combine like terms: 64n + -64n = 0
2 + -64n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -32n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -32n + 2n2)' equal to zero and attempt to solve:

Simplifying
1 + -32n + 2n2 = 0

Solving
1 + -32n + 2n2 = 0

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

Divide each side by '2'.
0.5 + -16n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -16n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -16n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -16n + n2 = 0 + -0.5
-16n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-16n + n2 = -0.5

The n term is -16n.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16n + 64 + n2 = -0.5 + 64

Reorder the terms:
64 + -16n + n2 = -0.5 + 64

Combine like terms: -0.5 + 64 = 63.5
64 + -16n + n2 = 63.5

Factor a perfect square on the left side:
(n + -8)(n + -8) = 63.5

Calculate the square root of the right side: 7.968688725

Break this problem into two subproblems by setting 
(n + -8) equal to 7.968688725 and -7.968688725.

Subproblem 1
n + -8 = 7.968688725

Simplifying
n + -8 = 7.968688725

Reorder the terms:
-8 + n = 7.968688725

Solving
-8 + n = 7.968688725

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + n = 7.968688725 + 8

Combine like terms: -8 + 8 = 0
0 + n = 7.968688725 + 8
n = 7.968688725 + 8

Combine like terms: 7.968688725 + 8 = 15.968688725
n = 15.968688725

Simplifying
n = 15.968688725

Subproblem 2
n + -8 = -7.968688725

Simplifying
n + -8 = -7.968688725

Reorder the terms:
-8 + n = -7.968688725

Solving
-8 + n = -7.968688725

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + n = -7.968688725 + 8

Combine like terms: -8 + 8 = 0
0 + n = -7.968688725 + 8
n = -7.968688725 + 8

Combine like terms: -7.968688725 + 8 = 0.031311275
n = 0.031311275

Simplifying
n = 0.031311275

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {15.968688725, 0.031311275}
Solution
n = {15.968688725, 0.031311275}