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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -4x + x = -3x
6 + -3x + 4x2 + -2x2 = -6 + -1x + 2x2 + 6 + x + -2x2

Combine like terms: 4x2 + -2x2 = 2x2
6 + -3x + 2x2 = -6 + -1x + 2x2 + 6 + x + -2x2

Reorder the terms:
6 + -3x + 2x2 = -6 + 6 + -1x + x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -3x + 2x2 = 0 + -1x + x + 2x2 + -2x2
6 + -3x + 2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
6 + -3x + 2x2 = 0 + 2x2 + -2x2
6 + -3x + 2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -3x + 2x2 = 0

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

Divide each side by '2'.
3 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1.5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -1.5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1.5x + x2 = 0 + -3
-1.5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1.5x + x2 = -3

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 = -3 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -3 + 0.5625

Combine like terms: -3 + 0.5625 = -2.4375
0.5625 + -1.5x + x2 = -2.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -2.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.