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

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


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

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

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

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

Reorder the terms:
(6 + -3X + -2x + xX) = (x + 1)(x + 2)
(6 + -3X + -2x + xX) = (x + 1)(x + 2)

Reorder the terms:
6 + -3X + -2x + xX = (1 + x)(x + 2)

Reorder the terms:
6 + -3X + -2x + xX = (1 + x)(2 + x)

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

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

Solving
6 + -3X + -2x + xX = 2 + 3x + x2

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -3X + -2x + -6 + xX = 2 + 3x + -6 + x2

Reorder the terms:
6 + -6 + -3X + -2x + xX = 2 + 3x + -6 + x2

Combine like terms: 6 + -6 = 0
0 + -3X + -2x + xX = 2 + 3x + -6 + x2
-3X + -2x + xX = 2 + 3x + -6 + x2

Reorder the terms:
-3X + -2x + xX = 2 + -6 + 3x + x2

Combine like terms: 2 + -6 = -4
-3X + -2x + xX = -4 + 3x + x2

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

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

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

Reorder the terms:
4 + -3X + -5x + xX + -1x2 = -4 + 5x + x2 + 4 + -5x + -1x2

Reorder the terms:
4 + -3X + -5x + xX + -1x2 = -4 + 4 + 5x + -5x + x2 + -1x2

Combine like terms: -4 + 4 = 0
4 + -3X + -5x + xX + -1x2 = 0 + 5x + -5x + x2 + -1x2
4 + -3X + -5x + xX + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
4 + -3X + -5x + xX + -1x2 = 0 + x2 + -1x2
4 + -3X + -5x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -3X + -5x + xX + -1x2 = 0

The solution to this equation could not be determined.

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