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

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


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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
-2 + 1x + x2 + -1x2 = 6 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x + 0 = 6 + -5x + x2 + -1x2
-2 + 1x = 6 + -5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 1x = 6 + -5x + 0
-2 + 1x = 6 + -5x

Solving
-2 + 1x = 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.
-2 + 1x + 5x = 6 + -5x + 5x

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

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

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

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

Combine like terms: 6 + 2 = 8
6x = 8

Divide each side by '6'.
x = 1.333333333

Simplifying
x = 1.333333333

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