-3X(-6+3X)=-6

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Solution for -3X(-6+3X)=-6 equation: 


Simplifying
-3X(-6 + 3X) = -6
(-6 * -3X + 3X * -3X) = -6
(18X + -9X2) = -6

Solving
18X + -9X2 = -6

Solving for variable 'X'.

Reorder the terms:
6 + 18X + -9X2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 18X + -9X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 6X + -3X2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + 6X + -3X2)' equal to zero and attempt to solve:

Simplifying
2 + 6X + -3X2 = 0

Solving
2 + 6X + -3X2 = 0

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

Divide each side by '-3'.
-0.6666666667 + -2X + X2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2X + 0.6666666667 + X2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2X + X2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2X + X2 = 0 + 0.6666666667
-2X + X2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2X + X2 = 0.6666666667

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 = 0.6666666667 + 1

Reorder the terms:
1 + -2X + X2 = 0.6666666667 + 1

Combine like terms: 0.6666666667 + 1 = 1.6666666667
1 + -2X + X2 = 1.6666666667

Factor a perfect square on the left side:
(X + -1)(X + -1) = 1.6666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(X + -1) equal to 1.290994449 and -1.290994449.


Subproblem 1
X + -1 = 1.290994449

Simplifying
X + -1 = 1.290994449

Reorder the terms:
-1 + X = 1.290994449

Solving
-1 + X = 1.290994449

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 = 1.290994449 + 1

Combine like terms: -1 + 1 = 0
0 + X = 1.290994449 + 1
X = 1.290994449 + 1

Combine like terms: 1.290994449 + 1 = 2.290994449
X = 2.290994449

Simplifying
X = 2.290994449


Subproblem 2
X + -1 = -1.290994449

Simplifying
X + -1 = -1.290994449

Reorder the terms:
-1 + X = -1.290994449

Solving
-1 + X = -1.290994449

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 = -1.290994449 + 1

Combine like terms: -1 + 1 = 0
0 + X = -1.290994449 + 1
X = -1.290994449 + 1

Combine like terms: -1.290994449 + 1 = -0.290994449
X = -0.290994449

Simplifying
X = -0.290994449


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.290994449, -0.290994449}
Solution
X = {2.290994449, -0.290994449}

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