-4n(n-3)=2(6-5n)+12n

Solution for -4n(n-3)=2(6-5n)+12n equation:

Simplifying
-4n(n + -3) = 2(6 + -5n) + 12n

Reorder the terms:
-4n(-3 + n) = 2(6 + -5n) + 12n
(-3 * -4n + n * -4n) = 2(6 + -5n) + 12n
(12n + -4n2) = 2(6 + -5n) + 12n
12n + -4n2 = (6 * 2 + -5n * 2) + 12n
12n + -4n2 = (12 + -10n) + 12n

Combine like terms: -10n + 12n = 2n
12n + -4n2 = 12 + 2n

Solving
12n + -4n2 = 12 + 2n

Solving for variable 'n'.

Reorder the terms:
-12 + 12n + -2n + -4n2 = 12 + 2n + -12 + -2n

Combine like terms: 12n + -2n = 10n
-12 + 10n + -4n2 = 12 + 2n + -12 + -2n

Reorder the terms:
-12 + 10n + -4n2 = 12 + -12 + 2n + -2n

Combine like terms: 12 + -12 = 0
-12 + 10n + -4n2 = 0 + 2n + -2n
-12 + 10n + -4n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-12 + 10n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5n + -2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 5n + -2n2)' equal to zero and attempt to solve:

Simplifying
-6 + 5n + -2n2 = 0

Solving
-6 + 5n + -2n2 = 0

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

Divide each side by '-2'.
3 + -2.5n + n2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2.5n + -3 + n2 = 0 + -3

Reorder the terms:
3 + -3 + -2.5n + n2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2.5n + n2 = 0 + -3
-2.5n + n2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2.5n + n2 = -3

The n term is -2.5n.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5n + 1.5625 + n2 = -3 + 1.5625

Reorder the terms:
1.5625 + -2.5n + n2 = -3 + 1.5625

Combine like terms: -3 + 1.5625 = -1.4375
1.5625 + -2.5n + n2 = -1.4375

Factor a perfect square on the left side:
(n + -1.25)(n + -1.25) = -1.4375

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.