3(x+2)=6x(x-1)-3

Solution for 3(x+2)=6x(x-1)-3 equation:

Simplifying
3(x + 2) = 6x(x + -1) + -3

Reorder the terms:
3(2 + x) = 6x(x + -1) + -3
(2 * 3 + x * 3) = 6x(x + -1) + -3
(6 + 3x) = 6x(x + -1) + -3

Reorder the terms:
6 + 3x = 6x(-1 + x) + -3
6 + 3x = (-1 * 6x + x * 6x) + -3
6 + 3x = (-6x + 6x2) + -3

Reorder the terms:
6 + 3x = -3 + -6x + 6x2

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

Solving for variable 'x'.

Reorder the terms:
6 + 3 + 3x + 6x + -6x2 = -3 + -6x + 6x2 + 3 + 6x + -6x2

Combine like terms: 6 + 3 = 9
9 + 3x + 6x + -6x2 = -3 + -6x + 6x2 + 3 + 6x + -6x2

Combine like terms: 3x + 6x = 9x
9 + 9x + -6x2 = -3 + -6x + 6x2 + 3 + 6x + -6x2

Reorder the terms:
9 + 9x + -6x2 = -3 + 3 + -6x + 6x + 6x2 + -6x2

Combine like terms: -3 + 3 = 0
9 + 9x + -6x2 = 0 + -6x + 6x + 6x2 + -6x2
9 + 9x + -6x2 = -6x + 6x + 6x2 + -6x2

Combine like terms: -6x + 6x = 0
9 + 9x + -6x2 = 0 + 6x2 + -6x2
9 + 9x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
9 + 9x + -6x2 = 0

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

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

Simplifying
3 + 3x + -2x2 = 0

Solving
3 + 3x + -2x2 = 0

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

Divide each side by '-2'.
-1.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.5x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.5x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.5x + x2 = 0 + 1.5
-1.5x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1.5x + x2 = 1.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 1.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.5 + 0.5625

Combine like terms: 1.5 + 0.5625 = 2.0625
0.5625 + -1.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + -0.75 = 1.436140662

Simplifying
x + -0.75 = 1.436140662

Reorder the terms:
-0.75 + x = 1.436140662

Solving
-0.75 + x = 1.436140662

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.436140662 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.436140662 + 0.75
x = 1.436140662 + 0.75

Combine like terms: 1.436140662 + 0.75 = 2.186140662
x = 2.186140662

Simplifying
x = 2.186140662

Subproblem 2
x + -0.75 = -1.436140662

Simplifying
x + -0.75 = -1.436140662

Reorder the terms:
-0.75 + x = -1.436140662

Solving
-0.75 + x = -1.436140662

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.436140662 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.436140662 + 0.75
x = -1.436140662 + 0.75

Combine like terms: -1.436140662 + 0.75 = -0.686140662
x = -0.686140662

Simplifying
x = -0.686140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.186140662, -0.686140662}
Solution
x = {2.186140662, -0.686140662}