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

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


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

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

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

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

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

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

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

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

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

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

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

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

Solving
2 + -3x = -3 + -2x

Solving for variable 'x'.

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

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

Combine like terms: -3x + 2x = -1x
2 + -1x = -3 + -2x + 2x

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

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

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

Combine like terms: -3 + -2 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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