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

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

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

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

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

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

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

Reorder the terms:
3 + -8x + 4x2 = (-2 + x)(4x + 3)

Reorder the terms:
3 + -8x + 4x2 = (-2 + x)(3 + 4x)

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

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

Add '-4x2' to each side of the equation.
3 + -8x + 4x2 + -4x2 = -6 + -5x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -8x + 0 = -6 + -5x + 4x2 + -4x2
3 + -8x = -6 + -5x + 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -8x = -6 + -5x + 0
3 + -8x = -6 + -5x

Solving
3 + -8x = -6 + -5x

Solving for variable 'x'.

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

Add '5x' to each side of the equation.
3 + -8x + 5x = -6 + -5x + 5x

Combine like terms: -8x + 5x = -3x
3 + -3x = -6 + -5x + 5x

Combine like terms: -5x + 5x = 0
3 + -3x = -6 + 0
3 + -3x = -6

Add '-3' to each side of the equation.
3 + -3 + -3x = -6 + -3

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

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

Divide each side by '-3'.
x = 3

Simplifying
x = 3