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

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

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

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

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

Multiply (-1 + 2x) * (-2 + x)
3x = (-1(-2 + x) + 2x * (-2 + x))
3x = ((-2 * -1 + x * -1) + 2x * (-2 + x))
3x = ((2 + -1x) + 2x * (-2 + x))
3x = (2 + -1x + (-2 * 2x + x * 2x))
3x = (2 + -1x + (-4x + 2x2))

Combine like terms: -1x + -4x = -5x
3x = (2 + -5x + 2x2)

Solving
3x = 2 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 3x + 5x + -2x2 = 2 + -5x + 2x2 + -2 + 5x + -2x2

Combine like terms: 3x + 5x = 8x
-2 + 8x + -2x2 = 2 + -5x + 2x2 + -2 + 5x + -2x2

Reorder the terms:
-2 + 8x + -2x2 = 2 + -2 + -5x + 5x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
-2 + 8x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2
-2 + 8x + -2x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-2 + 8x + -2x2 = 0 + 2x2 + -2x2
-2 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
-1 + 4x + -1x2 = 0

Solving
-1 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1 + -4x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -4x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x + x2 = 0 + -1
-4x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4x + x2 = -1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1 + 4

Reorder the terms:
4 + -4x + x2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4x + x2 = 3

Factor a perfect square on the left side:
(x + -2)(x + -2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1
x + -2 = 1.732050808

Simplifying
x + -2 = 1.732050808

Reorder the terms:
-2 + x = 1.732050808

Solving
-2 + x = 1.732050808

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.732050808 + 2
x = 1.732050808 + 2

Combine like terms: 1.732050808 + 2 = 3.732050808
x = 3.732050808

Simplifying
x = 3.732050808

Subproblem 2
x + -2 = -1.732050808

Simplifying
x + -2 = -1.732050808

Reorder the terms:
-2 + x = -1.732050808

Solving
-2 + x = -1.732050808

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.732050808 + 2
x = -1.732050808 + 2

Combine like terms: -1.732050808 + 2 = 0.267949192
x = 0.267949192

Simplifying
x = 0.267949192

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.732050808, 0.267949192}
Solution
x = {3.732050808, 0.267949192}