[2x-3][x-1]=[x-3][x-2]

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Solution for [2x-3][x-1]=[x-3][x-2] equation: 


Simplifying
[2x + -3][x + -1] = [x + -3][x + -2]

Reorder the terms:
[-3 + 2x][x + -1] = [x + -3][x + -2]

Reorder the terms:
[-3 + 2x][-1 + x] = [x + -3][x + -2]

Multiply [-3 + 2x] * [-1 + x]
[-3[-1 + x] + 2x * [-1 + x]] = [x + -3][x + -2]
[[-1 * -3 + x * -3] + 2x * [-1 + x]] = [x + -3][x + -2]
[[3 + -3x] + 2x * [-1 + x]] = [x + -3][x + -2]
[3 + -3x + [-1 * 2x + x * 2x]] = [x + -3][x + -2]
[3 + -3x + [-2x + 2x2]] = [x + -3][x + -2]

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

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

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

Multiply [-3 + x] * [-2 + x]
3 + -5x + 2x2 = [-3[-2 + x] + x[-2 + x]]
3 + -5x + 2x2 = [[-2 * -3 + x * -3] + x[-2 + x]]
3 + -5x + 2x2 = [[6 + -3x] + x[-2 + x]]
3 + -5x + 2x2 = [6 + -3x + [-2 * x + x * x]]
3 + -5x + 2x2 = [6 + -3x + [-2x + x2]]

Combine like terms: -3x + -2x = -5x
3 + -5x + 2x2 = [6 + -5x + x2]

Add '5x' to each side of the equation.
3 + -5x + 5x + 2x2 = 6 + -5x + 5x + x2

Combine like terms: -5x + 5x = 0
3 + 0 + 2x2 = 6 + -5x + 5x + x2
3 + 2x2 = 6 + -5x + 5x + x2

Combine like terms: -5x + 5x = 0
3 + 2x2 = 6 + 0 + x2
3 + 2x2 = 6 + x2

Solving
3 + 2x2 = 6 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
3 + 2x2 + -1x2 = 6 + x2 + -1x2

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

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

Add '-3' to each side of the equation.
3 + -3 + 1x2 = 6 + -3

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

Combine like terms: 6 + -3 = 3
1x2 = 3

Divide each side by '1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}

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