2(3n-15)n=14

Solution for 2(3n-15)n=14 equation:

Simplifying
2(3n + -15) * n = 14

Reorder the terms:
2(-15 + 3n) * n = 14

Reorder the terms for easier multiplication:
2n(-15 + 3n) = 14
(-15 * 2n + 3n * 2n) = 14
(-30n + 6n2) = 14

Solving
-30n + 6n2 = 14

Solving for variable 'n'.

Reorder the terms:
-14 + -30n + 6n2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -30n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -15n + 3n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -15n + 3n2)' equal to zero and attempt to solve:

Simplifying
-7 + -15n + 3n2 = 0

Solving
-7 + -15n + 3n2 = 0

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

Divide each side by '3'.
-2.333333333 + -5n + n2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -5n + 2.333333333 + n2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -5n + n2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -5n + n2 = 0 + 2.333333333
-5n + n2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-5n + n2 = 2.333333333

The n term is -5n.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5n + 6.25 + n2 = 2.333333333 + 6.25

Reorder the terms:
6.25 + -5n + n2 = 2.333333333 + 6.25

Combine like terms: 2.333333333 + 6.25 = 8.583333333
6.25 + -5n + n2 = 8.583333333

Factor a perfect square on the left side:
(n + -2.5)(n + -2.5) = 8.583333333

Calculate the square root of the right side: 2.929732638

Break this problem into two subproblems by setting 
(n + -2.5) equal to 2.929732638 and -2.929732638.

Subproblem 1
n + -2.5 = 2.929732638

Simplifying
n + -2.5 = 2.929732638

Reorder the terms:
-2.5 + n = 2.929732638

Solving
-2.5 + n = 2.929732638

Solving for variable 'n'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = 2.929732638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = 2.929732638 + 2.5
n = 2.929732638 + 2.5

Combine like terms: 2.929732638 + 2.5 = 5.429732638
n = 5.429732638

Simplifying
n = 5.429732638

Subproblem 2
n + -2.5 = -2.929732638

Simplifying
n + -2.5 = -2.929732638

Reorder the terms:
-2.5 + n = -2.929732638

Solving
-2.5 + n = -2.929732638

Solving for variable 'n'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + n = -2.929732638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + n = -2.929732638 + 2.5
n = -2.929732638 + 2.5

Combine like terms: -2.929732638 + 2.5 = -0.429732638
n = -0.429732638

Simplifying
n = -0.429732638

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.429732638, -0.429732638}
Solution
n = {5.429732638, -0.429732638}