7(2n-3)6n-12=

Solution for 7(2n-3)6n-12= equation:

Simplifying
7(2n + -3) * 6n + -12 = 0

Reorder the terms:
7(-3 + 2n) * 6n + -12 = 0

Reorder the terms for easier multiplication:
7 * 6n(-3 + 2n) + -12 = 0

Multiply 7 * 6
42n(-3 + 2n) + -12 = 0
(-3 * 42n + 2n * 42n) + -12 = 0
(-126n + 84n2) + -12 = 0

Reorder the terms:
-12 + -126n + 84n2 = 0

Solving
-12 + -126n + 84n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -21n + 14n2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -21n + 14n2)' equal to zero and attempt to solve:

Simplifying
-2 + -21n + 14n2 = 0

Solving
-2 + -21n + 14n2 = 0

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

Divide each side by '14'.
-0.1428571429 + -1.5n + n2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -1.5n + 0.1428571429 + n2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -1.5n + n2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -1.5n + n2 = 0 + 0.1428571429
-1.5n + n2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-1.5n + n2 = 0.1428571429

The n term is -1.5n.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5n + 0.5625 + n2 = 0.1428571429 + 0.5625

Reorder the terms:
0.5625 + -1.5n + n2 = 0.1428571429 + 0.5625

Combine like terms: 0.1428571429 + 0.5625 = 0.7053571429
0.5625 + -1.5n + n2 = 0.7053571429

Factor a perfect square on the left side:
(n + -0.75)(n + -0.75) = 0.7053571429

Calculate the square root of the right side: 0.83985543

Break this problem into two subproblems by setting 
(n + -0.75) equal to 0.83985543 and -0.83985543.

Subproblem 1
n + -0.75 = 0.83985543

Simplifying
n + -0.75 = 0.83985543

Reorder the terms:
-0.75 + n = 0.83985543

Solving
-0.75 + n = 0.83985543

Solving for variable 'n'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + n = 0.83985543 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + n = 0.83985543 + 0.75
n = 0.83985543 + 0.75

Combine like terms: 0.83985543 + 0.75 = 1.58985543
n = 1.58985543

Simplifying
n = 1.58985543

Subproblem 2
n + -0.75 = -0.83985543

Simplifying
n + -0.75 = -0.83985543

Reorder the terms:
-0.75 + n = -0.83985543

Solving
-0.75 + n = -0.83985543

Solving for variable 'n'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + n = -0.83985543 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + n = -0.83985543 + 0.75
n = -0.83985543 + 0.75

Combine like terms: -0.83985543 + 0.75 = -0.08985543
n = -0.08985543

Simplifying
n = -0.08985543

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.58985543, -0.08985543}
Solution
n = {1.58985543, -0.08985543}