3x-6=6x(x-3)

Solution for 3x-6=6x(x-3) equation:

Simplifying
3x + -6 = 6x(x + -3)

Reorder the terms:
-6 + 3x = 6x(x + -3)

Reorder the terms:
-6 + 3x = 6x(-3 + x)
-6 + 3x = (-3 * 6x + x * 6x)
-6 + 3x = (-18x + 6x2)

Solving
-6 + 3x = -18x + 6x2

Solving for variable 'x'.

Combine like terms: 3x + 18x = 21x
-6 + 21x + -6x2 = -18x + 6x2 + 18x + -6x2

Reorder the terms:
-6 + 21x + -6x2 = -18x + 18x + 6x2 + -6x2

Combine like terms: -18x + 18x = 0
-6 + 21x + -6x2 = 0 + 6x2 + -6x2
-6 + 21x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-6 + 21x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 7x + -2x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 7x + -2x2)' equal to zero and attempt to solve:

Simplifying
-2 + 7x + -2x2 = 0

Solving
-2 + 7x + -2x2 = 0

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

Divide each side by '-2'.
1 + -3.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -3.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3.5x + x2 = 0 + -1
-3.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3.5x + x2 = -1

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = -1 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = -1 + 3.0625

Combine like terms: -1 + 3.0625 = 2.0625
3.0625 + -3.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + -1.75 = 1.436140662

Simplifying
x + -1.75 = 1.436140662

Reorder the terms:
-1.75 + x = 1.436140662

Solving
-1.75 + x = 1.436140662

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = 1.436140662 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 1.436140662 + 1.75
x = 1.436140662 + 1.75

Combine like terms: 1.436140662 + 1.75 = 3.186140662
x = 3.186140662

Simplifying
x = 3.186140662

Subproblem 2
x + -1.75 = -1.436140662

Simplifying
x + -1.75 = -1.436140662

Reorder the terms:
-1.75 + x = -1.436140662

Solving
-1.75 + x = -1.436140662

Solving for variable 'x'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + x = -1.436140662 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -1.436140662 + 1.75
x = -1.436140662 + 1.75

Combine like terms: -1.436140662 + 1.75 = 0.313859338
x = 0.313859338

Simplifying
x = 0.313859338

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.186140662, 0.313859338}
Solution
x = {3.186140662, 0.313859338}