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

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

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

Reorder the terms:
3n(-2 + n) + -2(3 + -1n) = 4(n + -3)
(-2 * 3n + n * 3n) + -2(3 + -1n) = 4(n + -3)
(-6n + 3n2) + -2(3 + -1n) = 4(n + -3)
-6n + 3n2 + (3 * -2 + -1n * -2) = 4(n + -3)
-6n + 3n2 + (-6 + 2n) = 4(n + -3)

Reorder the terms:
-6 + -6n + 2n + 3n2 = 4(n + -3)

Combine like terms: -6n + 2n = -4n
-6 + -4n + 3n2 = 4(n + -3)

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

Solving
-6 + -4n + 3n2 = -12 + 4n

Solving for variable 'n'.

Reorder the terms:
-6 + 12 + -4n + -4n + 3n2 = -12 + 4n + 12 + -4n

Combine like terms: -6 + 12 = 6
6 + -4n + -4n + 3n2 = -12 + 4n + 12 + -4n

Combine like terms: -4n + -4n = -8n
6 + -8n + 3n2 = -12 + 4n + 12 + -4n

Reorder the terms:
6 + -8n + 3n2 = -12 + 12 + 4n + -4n

Combine like terms: -12 + 12 = 0
6 + -8n + 3n2 = 0 + 4n + -4n
6 + -8n + 3n2 = 4n + -4n

Combine like terms: 4n + -4n = 0
6 + -8n + 3n2 = 0

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

Divide each side by '3'.
2 + -2.666666667n + n2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2.666666667n + -2 + n2 = 0 + -2

Reorder the terms:
2 + -2 + -2.666666667n + n2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2.666666667n + n2 = 0 + -2
-2.666666667n + n2 = 0 + -2

Combine like terms: 0 + -2 = -2
-2.666666667n + n2 = -2

The n term is -2.666666667n.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667n + 1.777777780 + n2 = -2 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667n + n2 = -2 + 1.777777780

Combine like terms: -2 + 1.777777780 = -0.22222222
1.777777780 + -2.666666667n + n2 = -0.22222222

Factor a perfect square on the left side:
(n + -1.333333334)(n + -1.333333334) = -0.22222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.