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

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


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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
2 + -3x + x2 + -1x2 = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x + 0 = -6 + -1x + x2 + -1x2
2 + -3x = -6 + -1x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x = -6 + -1x + 0
2 + -3x = -6 + -1x

Solving
2 + -3x = -6 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
2 + -3x + x = -6 + -1x + x

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

Combine like terms: -1x + x = 0
2 + -2x = -6 + 0
2 + -2x = -6

Add '-2' to each side of the equation.
2 + -2 + -2x = -6 + -2

Combine like terms: 2 + -2 = 0
0 + -2x = -6 + -2
-2x = -6 + -2

Combine like terms: -6 + -2 = -8
-2x = -8

Divide each side by '-2'.
x = 4

Simplifying
x = 4

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