6x(x-1)=3(4x+2)

Solution for 6x(x-1)=3(4x+2) equation:

Simplifying
6x(x + -1) = 3(4x + 2)

Reorder the terms:
6x(-1 + x) = 3(4x + 2)
(-1 * 6x + x * 6x) = 3(4x + 2)
(-6x + 6x2) = 3(4x + 2)

Reorder the terms:
-6x + 6x2 = 3(2 + 4x)
-6x + 6x2 = (2 * 3 + 4x * 3)
-6x + 6x2 = (6 + 12x)

Solving
-6x + 6x2 = 6 + 12x

Solving for variable 'x'.

Reorder the terms:
-6 + -6x + -12x + 6x2 = 6 + 12x + -6 + -12x

Combine like terms: -6x + -12x = -18x
-6 + -18x + 6x2 = 6 + 12x + -6 + -12x

Reorder the terms:
-6 + -18x + 6x2 = 6 + -6 + 12x + -12x

Combine like terms: 6 + -6 = 0
-6 + -18x + 6x2 = 0 + 12x + -12x
-6 + -18x + 6x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-6 + -18x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -3x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -3x + x2 = 0

Solving
-1 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x + x2 = 0 + 1
-3x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3x + x2 = 1

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 1 + 2.25

Combine like terms: 1 + 2.25 = 3.25
2.25 + -3x + x2 = 3.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -1.5 = 1.802775638

Simplifying
x + -1.5 = 1.802775638

Reorder the terms:
-1.5 + x = 1.802775638

Solving
-1.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.802775638 + 1.5
x = 1.802775638 + 1.5

Combine like terms: 1.802775638 + 1.5 = 3.302775638
x = 3.302775638

Simplifying
x = 3.302775638

Subproblem 2
x + -1.5 = -1.802775638

Simplifying
x + -1.5 = -1.802775638

Reorder the terms:
-1.5 + x = -1.802775638

Solving
-1.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.802775638 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.802775638 + 1.5
x = -1.802775638 + 1.5

Combine like terms: -1.802775638 + 1.5 = -0.302775638
x = -0.302775638

Simplifying
x = -0.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.302775638, -0.302775638}
Solution
x = {3.302775638, -0.302775638}