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

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

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

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

Solving
6n + -3n2 = 3 + -2n

Solving for variable 'n'.

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

Combine like terms: 6n + 2n = 8n
-3 + 8n + -3n2 = 3 + -2n + -3 + 2n

Reorder the terms:
-3 + 8n + -3n2 = 3 + -3 + -2n + 2n

Combine like terms: 3 + -3 = 0
-3 + 8n + -3n2 = 0 + -2n + 2n
-3 + 8n + -3n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-3 + 8n + -3n2 = 0

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

Divide each side by '-3'.
1 + -2.666666667n + n2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.666666667n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + -2.666666667n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.666666667n + n2 = 0 + -1
-2.666666667n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.666666667n + n2 = -1

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 = -1 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667n + n2 = -1 + 1.777777780

Combine like terms: -1 + 1.777777780 = 0.77777778
1.777777780 + -2.666666667n + n2 = 0.77777778

Factor a perfect square on the left side:
(n + -1.333333334)(n + -1.333333334) = 0.77777778

Calculate the square root of the right side: 0.881917105

Break this problem into two subproblems by setting 
(n + -1.333333334) equal to 0.881917105 and -0.881917105.

Subproblem 1
n + -1.333333334 = 0.881917105

Simplifying
n + -1.333333334 = 0.881917105

Reorder the terms:
-1.333333334 + n = 0.881917105

Solving
-1.333333334 + n = 0.881917105

Solving for variable 'n'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + n = 0.881917105 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + n = 0.881917105 + 1.333333334
n = 0.881917105 + 1.333333334

Combine like terms: 0.881917105 + 1.333333334 = 2.215250439
n = 2.215250439

Simplifying
n = 2.215250439

Subproblem 2
n + -1.333333334 = -0.881917105

Simplifying
n + -1.333333334 = -0.881917105

Reorder the terms:
-1.333333334 + n = -0.881917105

Solving
-1.333333334 + n = -0.881917105

Solving for variable 'n'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + n = -0.881917105 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + n = -0.881917105 + 1.333333334
n = -0.881917105 + 1.333333334

Combine like terms: -0.881917105 + 1.333333334 = 0.451416229
n = 0.451416229

Simplifying
n = 0.451416229

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.215250439, 0.451416229}