2n-3n(n-1)=15-4n

Solution for 2n-3n(n-1)=15-4n equation:

Simplifying
2n + -3n(n + -1) = 15 + -4n

Reorder the terms:
2n + -3n(-1 + n) = 15 + -4n
2n + (-1 * -3n + n * -3n) = 15 + -4n
2n + (3n + -3n2) = 15 + -4n

Combine like terms: 2n + 3n = 5n
5n + -3n2 = 15 + -4n

Solving
5n + -3n2 = 15 + -4n

Solving for variable 'n'.

Reorder the terms:
-15 + 5n + 4n + -3n2 = 15 + -4n + -15 + 4n

Combine like terms: 5n + 4n = 9n
-15 + 9n + -3n2 = 15 + -4n + -15 + 4n

Reorder the terms:
-15 + 9n + -3n2 = 15 + -15 + -4n + 4n

Combine like terms: 15 + -15 = 0
-15 + 9n + -3n2 = 0 + -4n + 4n
-15 + 9n + -3n2 = -4n + 4n

Combine like terms: -4n + 4n = 0
-15 + 9n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 3n + -1n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 3n + -1n2)' equal to zero and attempt to solve:

Simplifying
-5 + 3n + -1n2 = 0

Solving
-5 + 3n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
5 + -3n + n2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -3n + -5 + n2 = 0 + -5

Reorder the terms:
5 + -5 + -3n + n2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n + n2 = 0 + -5
-3n + n2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3n + n2 = -5

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = -5 + 2.25

Reorder the terms:
2.25 + -3n + n2 = -5 + 2.25

Combine like terms: -5 + 2.25 = -2.75
2.25 + -3n + n2 = -2.75

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.