3X(X-2)=12

Solution for 3X(X-2)=12 equation:

Simplifying
3X(X + -2) = 12

Reorder the terms:
3X(-2 + X) = 12
(-2 * 3X + X * 3X) = 12
(-6X + 3X2) = 12

Solving
-6X + 3X2 = 12

Solving for variable 'X'.

Reorder the terms:
-12 + -6X + 3X2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -6X + 3X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -2X + X2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -2X + X2)' equal to zero and attempt to solve:

Simplifying
-4 + -2X + X2 = 0

Solving
-4 + -2X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2X + 4 + X2 = 0 + 4

Reorder the terms:
-4 + 4 + -2X + X2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2X + X2 = 0 + 4
-2X + X2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2X + X2 = 4

The X term is -2X.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2X + 1 + X2 = 4 + 1

Reorder the terms:
1 + -2X + X2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2X + X2 = 5

Factor a perfect square on the left side:
(X + -1)(X + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(X + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
X + -1 = 2.236067978

Simplifying
X + -1 = 2.236067978

Reorder the terms:
-1 + X = 2.236067978

Solving
-1 + X = 2.236067978

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + X = 2.236067978 + 1
X = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
X = 3.236067978

Simplifying
X = 3.236067978

Subproblem 2
X + -1 = -2.236067978

Simplifying
X + -1 = -2.236067978

Reorder the terms:
-1 + X = -2.236067978

Solving
-1 + X = -2.236067978

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1 + X = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + X = -2.236067978 + 1
X = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
X = -1.236067978

Simplifying
X = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.236067978, -1.236067978}
Solution
X = {3.236067978, -1.236067978}