-5n-2n(2n-4)=-6n+1

Solution for -5n-2n(2n-4)=-6n+1 equation:

Simplifying
-5n + -2n(2n + -4) = -6n + 1

Reorder the terms:
-5n + -2n(-4 + 2n) = -6n + 1
-5n + (-4 * -2n + 2n * -2n) = -6n + 1
-5n + (8n + -4n2) = -6n + 1

Combine like terms: -5n + 8n = 3n
3n + -4n2 = -6n + 1

Reorder the terms:
3n + -4n2 = 1 + -6n

Solving
3n + -4n2 = 1 + -6n

Solving for variable 'n'.

Reorder the terms:
-1 + 3n + 6n + -4n2 = 1 + -6n + -1 + 6n

Combine like terms: 3n + 6n = 9n
-1 + 9n + -4n2 = 1 + -6n + -1 + 6n

Reorder the terms:
-1 + 9n + -4n2 = 1 + -1 + -6n + 6n

Combine like terms: 1 + -1 = 0
-1 + 9n + -4n2 = 0 + -6n + 6n
-1 + 9n + -4n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
-1 + 9n + -4n2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -2.25n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2.25n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2.25n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2.25n + n2 = 0 + -0.25
-2.25n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2.25n + n2 = -0.25

The n term is -2.25n.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25n + 1.265625 + n2 = -0.25 + 1.265625

Reorder the terms:
1.265625 + -2.25n + n2 = -0.25 + 1.265625

Combine like terms: -0.25 + 1.265625 = 1.015625
1.265625 + -2.25n + n2 = 1.015625

Factor a perfect square on the left side:
(n + -1.125)(n + -1.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(n + -1.125) equal to 1.007782219 and -1.007782219.

Subproblem 1
n + -1.125 = 1.007782219

Simplifying
n + -1.125 = 1.007782219

Reorder the terms:
-1.125 + n = 1.007782219

Solving
-1.125 + n = 1.007782219

Solving for variable 'n'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + n = 1.007782219 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + n = 1.007782219 + 1.125
n = 1.007782219 + 1.125

Combine like terms: 1.007782219 + 1.125 = 2.132782219
n = 2.132782219

Simplifying
n = 2.132782219

Subproblem 2
n + -1.125 = -1.007782219

Simplifying
n + -1.125 = -1.007782219

Reorder the terms:
-1.125 + n = -1.007782219

Solving
-1.125 + n = -1.007782219

Solving for variable 'n'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + n = -1.007782219 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + n = -1.007782219 + 1.125
n = -1.007782219 + 1.125

Combine like terms: -1.007782219 + 1.125 = 0.117217781
n = 0.117217781

Simplifying
n = 0.117217781

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.132782219, 0.117217781}