2n^2-4n*5n-10n+4=

Solution for 2n^2-4n*5n-10n+4= equation:

Simplifying
2n2 + -4n * 5n + -10n + 4 = 0

Reorder the terms for easier multiplication:
2n2 + -4 * 5n * n + -10n + 4 = 0

Multiply -4 * 5
2n2 + -20n * n + -10n + 4 = 0

Multiply n * n
2n2 + -20n2 + -10n + 4 = 0

Reorder the terms:
4 + -10n + 2n2 + -20n2 = 0

Combine like terms: 2n2 + -20n2 = -18n2
4 + -10n + -18n2 = 0

Solving
4 + -10n + -18n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5n + -9n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -5n + -9n2)' equal to zero and attempt to solve:

Simplifying
2 + -5n + -9n2 = 0

Solving
2 + -5n + -9n2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.2222222222 + 0.5555555556n + n2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + 0.5555555556n + 0.2222222222 + n2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + 0.5555555556n + n2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + 0.5555555556n + n2 = 0 + 0.2222222222
0.5555555556n + n2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
0.5555555556n + n2 = 0.2222222222

The n term is 0.5555555556n.  Take half its coefficient (0.2777777778).
Square it (0.07716049384) and add it to both sides.

Add '0.07716049384' to each side of the equation.
0.5555555556n + 0.07716049384 + n2 = 0.2222222222 + 0.07716049384

Reorder the terms:
0.07716049384 + 0.5555555556n + n2 = 0.2222222222 + 0.07716049384

Combine like terms: 0.2222222222 + 0.07716049384 = 0.29938271604
0.07716049384 + 0.5555555556n + n2 = 0.29938271604

Factor a perfect square on the left side:
(n + 0.2777777778)(n + 0.2777777778) = 0.29938271604

Calculate the square root of the right side: 0.547158767

Break this problem into two subproblems by setting 
(n + 0.2777777778) equal to 0.547158767 and -0.547158767.

Subproblem 1
n + 0.2777777778 = 0.547158767

Simplifying
n + 0.2777777778 = 0.547158767

Reorder the terms:
0.2777777778 + n = 0.547158767

Solving
0.2777777778 + n = 0.547158767

Solving for variable 'n'.

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

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -0.2777777778 + n = 0.547158767 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + n = 0.547158767 + -0.2777777778
n = 0.547158767 + -0.2777777778

Combine like terms: 0.547158767 + -0.2777777778 = 0.2693809892
n = 0.2693809892

Simplifying
n = 0.2693809892

Subproblem 2
n + 0.2777777778 = -0.547158767

Simplifying
n + 0.2777777778 = -0.547158767

Reorder the terms:
0.2777777778 + n = -0.547158767

Solving
0.2777777778 + n = -0.547158767

Solving for variable 'n'.

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

Add '-0.2777777778' to each side of the equation.
0.2777777778 + -0.2777777778 + n = -0.547158767 + -0.2777777778

Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000
0.0000000000 + n = -0.547158767 + -0.2777777778
n = -0.547158767 + -0.2777777778

Combine like terms: -0.547158767 + -0.2777777778 = -0.8249365448
n = -0.8249365448

Simplifying
n = -0.8249365448

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.2693809892, -0.8249365448}
Solution
n = {0.2693809892, -0.8249365448}