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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply (-3 + x) * (-2 + x)
-2 + -1x + x2 = 3 + -4x + x2 + -1(-3(-2 + x) + x(-2 + x))
-2 + -1x + x2 = 3 + -4x + x2 + -1((-2 * -3 + x * -3) + x(-2 + x))
-2 + -1x + x2 = 3 + -4x + x2 + -1((6 + -3x) + x(-2 + x))
-2 + -1x + x2 = 3 + -4x + x2 + -1(6 + -3x + (-2 * x + x * x))
-2 + -1x + x2 = 3 + -4x + x2 + -1(6 + -3x + (-2x + x2))

Combine like terms: -3x + -2x = -5x
-2 + -1x + x2 = 3 + -4x + x2 + -1(6 + -5x + x2)
-2 + -1x + x2 = 3 + -4x + x2 + (6 * -1 + -5x * -1 + x2 * -1)
-2 + -1x + x2 = 3 + -4x + x2 + (-6 + 5x + -1x2)

Reorder the terms:
-2 + -1x + x2 = 3 + -6 + -4x + 5x + x2 + -1x2

Combine like terms: 3 + -6 = -3
-2 + -1x + x2 = -3 + -4x + 5x + x2 + -1x2

Combine like terms: -4x + 5x = 1x
-2 + -1x + x2 = -3 + 1x + x2 + -1x2

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

Solving
-2 + -1x + x2 = -3 + 1x

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {1, 1}