(4n+6)(2n)=60

Solution for (4n+6)(2n)=60 equation:

Simplifying
(4n + 6)(2n) = 60

Reorder the terms:
(6 + 4n)(2n) = 60

Remove parenthesis around (2n)
(6 + 4n) * 2n = 60

Reorder the terms for easier multiplication:
2n(6 + 4n) = 60
(6 * 2n + 4n * 2n) = 60
(12n + 8n2) = 60

Solving
12n + 8n2 = 60

Solving for variable 'n'.

Reorder the terms:
-60 + 12n + 8n2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 12n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 3n + 2n2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-15 + 3n + 2n2)' equal to zero and attempt to solve:

Simplifying
-15 + 3n + 2n2 = 0

Solving
-15 + 3n + 2n2 = 0

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

Divide each side by '2'.
-7.5 + 1.5n + n2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 1.5n + 7.5 + n2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 1.5n + n2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 1.5n + n2 = 0 + 7.5
1.5n + n2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
1.5n + n2 = 7.5

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 = 7.5 + 0.5625

Reorder the terms:
0.5625 + 1.5n + n2 = 7.5 + 0.5625

Combine like terms: 7.5 + 0.5625 = 8.0625
0.5625 + 1.5n + n2 = 8.0625

Factor a perfect square on the left side:
(n + 0.75)(n + 0.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(n + 0.75) equal to 2.839454173 and -2.839454173.

Subproblem 1
n + 0.75 = 2.839454173

Simplifying
n + 0.75 = 2.839454173

Reorder the terms:
0.75 + n = 2.839454173

Solving
0.75 + n = 2.839454173

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 = 2.839454173 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + n = 2.839454173 + -0.75
n = 2.839454173 + -0.75

Combine like terms: 2.839454173 + -0.75 = 2.089454173
n = 2.089454173

Simplifying
n = 2.089454173

Subproblem 2
n + 0.75 = -2.839454173

Simplifying
n + 0.75 = -2.839454173

Reorder the terms:
0.75 + n = -2.839454173

Solving
0.75 + n = -2.839454173

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 = -2.839454173 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + n = -2.839454173 + -0.75
n = -2.839454173 + -0.75

Combine like terms: -2.839454173 + -0.75 = -3.589454173
n = -3.589454173

Simplifying
n = -3.589454173

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.089454173, -3.589454173}
Solution
n = {2.089454173, -3.589454173}