-3(n-4)(1+5n)=n-3+5n

Solution for -3(n-4)(1+5n)=n-3+5n equation:

Simplifying
-3(n + -4)(1 + 5n) = n + -3 + 5n

Reorder the terms:
-3(-4 + n)(1 + 5n) = n + -3 + 5n

Multiply (-4 + n) * (1 + 5n)
-3(-4(1 + 5n) + n(1 + 5n)) = n + -3 + 5n
-3((1 * -4 + 5n * -4) + n(1 + 5n)) = n + -3 + 5n
-3((-4 + -20n) + n(1 + 5n)) = n + -3 + 5n
-3(-4 + -20n + (1 * n + 5n * n)) = n + -3 + 5n
-3(-4 + -20n + (1n + 5n2)) = n + -3 + 5n

Combine like terms: -20n + 1n = -19n
-3(-4 + -19n + 5n2) = n + -3 + 5n
(-4 * -3 + -19n * -3 + 5n2 * -3) = n + -3 + 5n
(12 + 57n + -15n2) = n + -3 + 5n

Reorder the terms:
12 + 57n + -15n2 = -3 + n + 5n

Combine like terms: n + 5n = 6n
12 + 57n + -15n2 = -3 + 6n

Solving
12 + 57n + -15n2 = -3 + 6n

Solving for variable 'n'.

Reorder the terms:
12 + 3 + 57n + -6n + -15n2 = -3 + 6n + 3 + -6n

Combine like terms: 12 + 3 = 15
15 + 57n + -6n + -15n2 = -3 + 6n + 3 + -6n

Combine like terms: 57n + -6n = 51n
15 + 51n + -15n2 = -3 + 6n + 3 + -6n

Reorder the terms:
15 + 51n + -15n2 = -3 + 3 + 6n + -6n

Combine like terms: -3 + 3 = 0
15 + 51n + -15n2 = 0 + 6n + -6n
15 + 51n + -15n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
15 + 51n + -15n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 17n + -5n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + 17n + -5n2)' equal to zero and attempt to solve:

Simplifying
5 + 17n + -5n2 = 0

Solving
5 + 17n + -5n2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1 + -3.4n + n2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.4n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.4n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.4n + n2 = 0 + 1
-3.4n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.4n + n2 = 1

The n term is -3.4n.  Take half its coefficient (-1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
-3.4n + 2.89 + n2 = 1 + 2.89

Reorder the terms:
2.89 + -3.4n + n2 = 1 + 2.89

Combine like terms: 1 + 2.89 = 3.89
2.89 + -3.4n + n2 = 3.89

Factor a perfect square on the left side:
(n + -1.7)(n + -1.7) = 3.89

Calculate the square root of the right side: 1.972308292

Break this problem into two subproblems by setting 
(n + -1.7) equal to 1.972308292 and -1.972308292.

Subproblem 1
n + -1.7 = 1.972308292

Simplifying
n + -1.7 = 1.972308292

Reorder the terms:
-1.7 + n = 1.972308292

Solving
-1.7 + n = 1.972308292

Solving for variable 'n'.

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

Add '1.7' to each side of the equation.
-1.7 + 1.7 + n = 1.972308292 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + n = 1.972308292 + 1.7
n = 1.972308292 + 1.7

Combine like terms: 1.972308292 + 1.7 = 3.672308292
n = 3.672308292

Simplifying
n = 3.672308292

Subproblem 2
n + -1.7 = -1.972308292

Simplifying
n + -1.7 = -1.972308292

Reorder the terms:
-1.7 + n = -1.972308292

Solving
-1.7 + n = -1.972308292

Solving for variable 'n'.

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

Add '1.7' to each side of the equation.
-1.7 + 1.7 + n = -1.972308292 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + n = -1.972308292 + 1.7
n = -1.972308292 + 1.7

Combine like terms: -1.972308292 + 1.7 = -0.272308292
n = -0.272308292

Simplifying
n = -0.272308292

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.672308292, -0.272308292}
Solution
n = {3.672308292, -0.272308292}