-7n(3n-8)=4(1-6n)

Solution for -7n(3n-8)=4(1-6n) equation:

Simplifying
-7n(3n + -8) = 4(1 + -6n)

Reorder the terms:
-7n(-8 + 3n) = 4(1 + -6n)
(-8 * -7n + 3n * -7n) = 4(1 + -6n)
(56n + -21n2) = 4(1 + -6n)
56n + -21n2 = (1 * 4 + -6n * 4)
56n + -21n2 = (4 + -24n)

Solving
56n + -21n2 = 4 + -24n

Solving for variable 'n'.

Reorder the terms:
-4 + 56n + 24n + -21n2 = 4 + -24n + -4 + 24n

Combine like terms: 56n + 24n = 80n
-4 + 80n + -21n2 = 4 + -24n + -4 + 24n

Reorder the terms:
-4 + 80n + -21n2 = 4 + -4 + -24n + 24n

Combine like terms: 4 + -4 = 0
-4 + 80n + -21n2 = 0 + -24n + 24n
-4 + 80n + -21n2 = -24n + 24n

Combine like terms: -24n + 24n = 0
-4 + 80n + -21n2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
0.1904761905 + -3.80952381n + n2 = 0

Move the constant term to the right:

Add '-0.1904761905' to each side of the equation.
0.1904761905 + -3.80952381n + -0.1904761905 + n2 = 0 + -0.1904761905

Reorder the terms:
0.1904761905 + -0.1904761905 + -3.80952381n + n2 = 0 + -0.1904761905

Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000
0.0000000000 + -3.80952381n + n2 = 0 + -0.1904761905
-3.80952381n + n2 = 0 + -0.1904761905

Combine like terms: 0 + -0.1904761905 = -0.1904761905
-3.80952381n + n2 = -0.1904761905

The n term is -3.80952381n.  Take half its coefficient (-1.904761905).
Square it (3.628117915) and add it to both sides.

Add '3.628117915' to each side of the equation.
-3.80952381n + 3.628117915 + n2 = -0.1904761905 + 3.628117915

Reorder the terms:
3.628117915 + -3.80952381n + n2 = -0.1904761905 + 3.628117915

Combine like terms: -0.1904761905 + 3.628117915 = 3.4376417245
3.628117915 + -3.80952381n + n2 = 3.4376417245

Factor a perfect square on the left side:
(n + -1.904761905)(n + -1.904761905) = 3.4376417245

Calculate the square root of the right side: 1.854087842

Break this problem into two subproblems by setting 
(n + -1.904761905) equal to 1.854087842 and -1.854087842.

Subproblem 1
n + -1.904761905 = 1.854087842

Simplifying
n + -1.904761905 = 1.854087842

Reorder the terms:
-1.904761905 + n = 1.854087842

Solving
-1.904761905 + n = 1.854087842

Solving for variable 'n'.

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

Add '1.904761905' to each side of the equation.
-1.904761905 + 1.904761905 + n = 1.854087842 + 1.904761905

Combine like terms: -1.904761905 + 1.904761905 = 0.000000000
0.000000000 + n = 1.854087842 + 1.904761905
n = 1.854087842 + 1.904761905

Combine like terms: 1.854087842 + 1.904761905 = 3.758849747
n = 3.758849747

Simplifying
n = 3.758849747

Subproblem 2
n + -1.904761905 = -1.854087842

Simplifying
n + -1.904761905 = -1.854087842

Reorder the terms:
-1.904761905 + n = -1.854087842

Solving
-1.904761905 + n = -1.854087842

Solving for variable 'n'.

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

Add '1.904761905' to each side of the equation.
-1.904761905 + 1.904761905 + n = -1.854087842 + 1.904761905

Combine like terms: -1.904761905 + 1.904761905 = 0.000000000
0.000000000 + n = -1.854087842 + 1.904761905
n = -1.854087842 + 1.904761905

Combine like terms: -1.854087842 + 1.904761905 = 0.050674063
n = 0.050674063

Simplifying
n = 0.050674063

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.758849747, 0.050674063}