960=(3n-2)*(2n)

Solution for 960=(3n-2)*(2n) equation:

Simplifying
960 = (3n + -2)(2n)

Reorder the terms:
960 = (-2 + 3n)(2n)

Remove parenthesis around (2n)
960 = (-2 + 3n) * 2n

Reorder the terms for easier multiplication:
960 = 2n(-2 + 3n)
960 = (-2 * 2n + 3n * 2n)
960 = (-4n + 6n2)

Solving
960 = -4n + 6n2

Solving for variable 'n'.

Reorder the terms:
960 + 4n + -6n2 = -4n + 4n + 6n2 + -6n2

Combine like terms: -4n + 4n = 0
960 + 4n + -6n2 = 0 + 6n2 + -6n2
960 + 4n + -6n2 = 6n2 + -6n2

Combine like terms: 6n2 + -6n2 = 0
960 + 4n + -6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(480 + 2n + -3n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(480 + 2n + -3n2)' equal to zero and attempt to solve:

Simplifying
480 + 2n + -3n2 = 0

Solving
480 + 2n + -3n2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-160 + -0.6666666667n + n2 = 0

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + -0.6666666667n + 160 + n2 = 0 + 160

Reorder the terms:
-160 + 160 + -0.6666666667n + n2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + -0.6666666667n + n2 = 0 + 160
-0.6666666667n + n2 = 0 + 160

Combine like terms: 0 + 160 = 160
-0.6666666667n + n2 = 160

The n term is -0.6666666667n.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667n + 0.1111111112 + n2 = 160 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667n + n2 = 160 + 0.1111111112

Combine like terms: 160 + 0.1111111112 = 160.1111111112
0.1111111112 + -0.6666666667n + n2 = 160.1111111112

Factor a perfect square on the left side:
(n + -0.3333333334)(n + -0.3333333334) = 160.1111111112

Calculate the square root of the right side: 12.653501931

Break this problem into two subproblems by setting 
(n + -0.3333333334) equal to 12.653501931 and -12.653501931.

Subproblem 1
n + -0.3333333334 = 12.653501931

Simplifying
n + -0.3333333334 = 12.653501931

Reorder the terms:
-0.3333333334 + n = 12.653501931

Solving
-0.3333333334 + n = 12.653501931

Solving for variable 'n'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + n = 12.653501931 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + n = 12.653501931 + 0.3333333334
n = 12.653501931 + 0.3333333334

Combine like terms: 12.653501931 + 0.3333333334 = 12.9868352644
n = 12.9868352644

Simplifying
n = 12.9868352644

Subproblem 2
n + -0.3333333334 = -12.653501931

Simplifying
n + -0.3333333334 = -12.653501931

Reorder the terms:
-0.3333333334 + n = -12.653501931

Solving
-0.3333333334 + n = -12.653501931

Solving for variable 'n'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + n = -12.653501931 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + n = -12.653501931 + 0.3333333334
n = -12.653501931 + 0.3333333334

Combine like terms: -12.653501931 + 0.3333333334 = -12.3201685976
n = -12.3201685976

Simplifying
n = -12.3201685976

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {12.9868352644, -12.3201685976}
Solution
n = {12.9868352644, -12.3201685976}