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

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


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

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

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

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

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

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

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

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

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

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

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

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

Solving
-2 + -1x = 1 + -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 + -1x + 2x = 1 + -2x + 2x

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

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

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

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

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

Divide each side by '1'.
x = 3

Simplifying
x = 3

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