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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
4 + -3x + x2 + -1x2 = 2 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -3x + 0 = 2 + -2x + x2 + -1x2
4 + -3x = 2 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -3x = 2 + -2x + 0
4 + -3x = 2 + -2x

Solving
4 + -3x = 2 + -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.
4 + -3x + 2x = 2 + -2x + 2x

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

Combine like terms: -2x + 2x = 0
4 + -1x = 2 + 0
4 + -1x = 2

Add '-4' to each side of the equation.
4 + -4 + -1x = 2 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 2 + -4
-1x = 2 + -4

Combine like terms: 2 + -4 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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