6(2n-3)2(6n+1)=10n

Solution for 6(2n-3)2(6n+1)=10n equation:

Simplifying
6(2n + -3) * 2(6n + 1) = 10n

Reorder the terms:
6(-3 + 2n) * 2(6n + 1) = 10n

Reorder the terms:
6(-3 + 2n) * 2(1 + 6n) = 10n

Reorder the terms for easier multiplication:
6 * 2(-3 + 2n)(1 + 6n) = 10n

Multiply 6 * 2
12(-3 + 2n)(1 + 6n) = 10n

Multiply (-3 + 2n) * (1 + 6n)
12(-3(1 + 6n) + 2n * (1 + 6n)) = 10n
12((1 * -3 + 6n * -3) + 2n * (1 + 6n)) = 10n
12((-3 + -18n) + 2n * (1 + 6n)) = 10n
12(-3 + -18n + (1 * 2n + 6n * 2n)) = 10n
12(-3 + -18n + (2n + 12n2)) = 10n

Combine like terms: -18n + 2n = -16n
12(-3 + -16n + 12n2) = 10n
(-3 * 12 + -16n * 12 + 12n2 * 12) = 10n
(-36 + -192n + 144n2) = 10n

Solving
-36 + -192n + 144n2 = 10n

Solving for variable 'n'.

Reorder the terms:
-36 + -192n + -10n + 144n2 = 10n + -10n

Combine like terms: -192n + -10n = -202n
-36 + -202n + 144n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-36 + -202n + 144n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -101n + 72n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-18 + -101n + 72n2)' equal to zero and attempt to solve:

Simplifying
-18 + -101n + 72n2 = 0

Solving
-18 + -101n + 72n2 = 0

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

Divide each side by '72'.
-0.25 + -1.402777778n + n2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.402777778n + 0.25 + n2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.402777778n + n2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.402777778n + n2 = 0 + 0.25
-1.402777778n + n2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.402777778n + n2 = 0.25

The n term is -1.402777778n.  Take half its coefficient (-0.701388889).
Square it (0.4919463736) and add it to both sides.

Add '0.4919463736' to each side of the equation.
-1.402777778n + 0.4919463736 + n2 = 0.25 + 0.4919463736

Reorder the terms:
0.4919463736 + -1.402777778n + n2 = 0.25 + 0.4919463736

Combine like terms: 0.25 + 0.4919463736 = 0.7419463736
0.4919463736 + -1.402777778n + n2 = 0.7419463736

Factor a perfect square on the left side:
(n + -0.701388889)(n + -0.701388889) = 0.7419463736

Calculate the square root of the right side: 0.86136309

Break this problem into two subproblems by setting 
(n + -0.701388889) equal to 0.86136309 and -0.86136309.

Subproblem 1
n + -0.701388889 = 0.86136309

Simplifying
n + -0.701388889 = 0.86136309

Reorder the terms:
-0.701388889 + n = 0.86136309

Solving
-0.701388889 + n = 0.86136309

Solving for variable 'n'.

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

Add '0.701388889' to each side of the equation.
-0.701388889 + 0.701388889 + n = 0.86136309 + 0.701388889

Combine like terms: -0.701388889 + 0.701388889 = 0.000000000
0.000000000 + n = 0.86136309 + 0.701388889
n = 0.86136309 + 0.701388889

Combine like terms: 0.86136309 + 0.701388889 = 1.562751979
n = 1.562751979

Simplifying
n = 1.562751979

Subproblem 2
n + -0.701388889 = -0.86136309

Simplifying
n + -0.701388889 = -0.86136309

Reorder the terms:
-0.701388889 + n = -0.86136309

Solving
-0.701388889 + n = -0.86136309

Solving for variable 'n'.

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

Add '0.701388889' to each side of the equation.
-0.701388889 + 0.701388889 + n = -0.86136309 + 0.701388889

Combine like terms: -0.701388889 + 0.701388889 = 0.000000000
0.000000000 + n = -0.86136309 + 0.701388889
n = -0.86136309 + 0.701388889

Combine like terms: -0.86136309 + 0.701388889 = -0.159974201
n = -0.159974201

Simplifying
n = -0.159974201

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.562751979, -0.159974201}
Solution
n = {1.562751979, -0.159974201}