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

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


Simplifying
(x2 + 3x + 2)(x + -3) = (x + -2)(x2 + 2x + 1)

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

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

Multiply (2 + 3x + x2) * (-3 + x)
(2(-3 + x) + 3x * (-3 + x) + x2(-3 + x)) = (x + -2)(x2 + 2x + 1)
((-3 * 2 + x * 2) + 3x * (-3 + x) + x2(-3 + x)) = (x + -2)(x2 + 2x + 1)
((-6 + 2x) + 3x * (-3 + x) + x2(-3 + x)) = (x + -2)(x2 + 2x + 1)
(-6 + 2x + (-3 * 3x + x * 3x) + x2(-3 + x)) = (x + -2)(x2 + 2x + 1)
(-6 + 2x + (-9x + 3x2) + x2(-3 + x)) = (x + -2)(x2 + 2x + 1)
(-6 + 2x + -9x + 3x2 + (-3 * x2 + x * x2)) = (x + -2)(x2 + 2x + 1)
(-6 + 2x + -9x + 3x2 + (-3x2 + x3)) = (x + -2)(x2 + 2x + 1)

Combine like terms: 2x + -9x = -7x
(-6 + -7x + 3x2 + -3x2 + x3) = (x + -2)(x2 + 2x + 1)

Combine like terms: 3x2 + -3x2 = 0
(-6 + -7x + 0 + x3) = (x + -2)(x2 + 2x + 1)
(-6 + -7x + x3) = (x + -2)(x2 + 2x + 1)

Reorder the terms:
-6 + -7x + x3 = (-2 + x)(x2 + 2x + 1)

Reorder the terms:
-6 + -7x + x3 = (-2 + x)(1 + 2x + x2)

Multiply (-2 + x) * (1 + 2x + x2)
-6 + -7x + x3 = (-2(1 + 2x + x2) + x(1 + 2x + x2))
-6 + -7x + x3 = ((1 * -2 + 2x * -2 + x2 * -2) + x(1 + 2x + x2))
-6 + -7x + x3 = ((-2 + -4x + -2x2) + x(1 + 2x + x2))
-6 + -7x + x3 = (-2 + -4x + -2x2 + (1 * x + 2x * x + x2 * x))
-6 + -7x + x3 = (-2 + -4x + -2x2 + (1x + 2x2 + x3))

Reorder the terms:
-6 + -7x + x3 = (-2 + -4x + 1x + -2x2 + 2x2 + x3)

Combine like terms: -4x + 1x = -3x
-6 + -7x + x3 = (-2 + -3x + -2x2 + 2x2 + x3)

Combine like terms: -2x2 + 2x2 = 0
-6 + -7x + x3 = (-2 + -3x + 0 + x3)
-6 + -7x + x3 = (-2 + -3x + x3)

Add '-1x3' to each side of the equation.
-6 + -7x + x3 + -1x3 = -2 + -3x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-6 + -7x + 0 = -2 + -3x + x3 + -1x3
-6 + -7x = -2 + -3x + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-6 + -7x = -2 + -3x + 0
-6 + -7x = -2 + -3x

Solving
-6 + -7x = -2 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-6 + -7x + 3x = -2 + -3x + 3x

Combine like terms: -7x + 3x = -4x
-6 + -4x = -2 + -3x + 3x

Combine like terms: -3x + 3x = 0
-6 + -4x = -2 + 0
-6 + -4x = -2

Add '6' to each side of the equation.
-6 + 6 + -4x = -2 + 6

Combine like terms: -6 + 6 = 0
0 + -4x = -2 + 6
-4x = -2 + 6

Combine like terms: -2 + 6 = 4
-4x = 4

Divide each side by '-4'.
x = -1

Simplifying
x = -1

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