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

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

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

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

Remove parenthesis around (-1 + 2x)
-1 + 2x = (x + -2)(4x + 3)

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

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

Multiply (-2 + x) * (3 + 4x)
-1 + 2x = (-2(3 + 4x) + x(3 + 4x))
-1 + 2x = ((3 * -2 + 4x * -2) + x(3 + 4x))
-1 + 2x = ((-6 + -8x) + x(3 + 4x))
-1 + 2x = (-6 + -8x + (3 * x + 4x * x))
-1 + 2x = (-6 + -8x + (3x + 4x2))

Combine like terms: -8x + 3x = -5x
-1 + 2x = (-6 + -5x + 4x2)

Solving
-1 + 2x = -6 + -5x + 4x2

Solving for variable 'x'.

Reorder the terms:
-1 + 6 + 2x + 5x + -4x2 = -6 + -5x + 4x2 + 6 + 5x + -4x2

Combine like terms: -1 + 6 = 5
5 + 2x + 5x + -4x2 = -6 + -5x + 4x2 + 6 + 5x + -4x2

Combine like terms: 2x + 5x = 7x
5 + 7x + -4x2 = -6 + -5x + 4x2 + 6 + 5x + -4x2

Reorder the terms:
5 + 7x + -4x2 = -6 + 6 + -5x + 5x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
5 + 7x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2
5 + 7x + -4x2 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
5 + 7x + -4x2 = 0 + 4x2 + -4x2
5 + 7x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5 + 7x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-1.25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.75x + x2 = 0 + 1.25
-1.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.75x + x2 = 1.25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1.25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1.25 + 0.765625

Combine like terms: 1.25 + 0.765625 = 2.015625
0.765625 + -1.75x + x2 = 2.015625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.419727086 and -1.419727086.

Subproblem 1
x + -0.875 = 1.419727086

Simplifying
x + -0.875 = 1.419727086

Reorder the terms:
-0.875 + x = 1.419727086

Solving
-0.875 + x = 1.419727086

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 1.419727086 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 1.419727086 + 0.875
x = 1.419727086 + 0.875

Combine like terms: 1.419727086 + 0.875 = 2.294727086
x = 2.294727086

Simplifying
x = 2.294727086

Subproblem 2
x + -0.875 = -1.419727086

Simplifying
x + -0.875 = -1.419727086

Reorder the terms:
-0.875 + x = -1.419727086

Solving
-0.875 + x = -1.419727086

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -1.419727086 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -1.419727086 + 0.875
x = -1.419727086 + 0.875

Combine like terms: -1.419727086 + 0.875 = -0.544727086
x = -0.544727086

Simplifying
x = -0.544727086

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.294727086, -0.544727086}