(x-2)(x-3)-3(x+2)=x(x-3)-6(x-2)

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Solution for (x-2)(x-3)-3(x+2)=x(x-3)-6(x-2) equation: 


Simplifying
(x + -2)(x + -3) + -3(x + 2) = x(x + -3) + -6(x + -2)

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

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

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

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

Reorder the terms:
6 + -5x + x2 + -3(2 + x) = x(x + -3) + -6(x + -2)
6 + -5x + x2 + (2 * -3 + x * -3) = x(x + -3) + -6(x + -2)
6 + -5x + x2 + (-6 + -3x) = x(x + -3) + -6(x + -2)

Reorder the terms:
6 + -6 + -5x + -3x + x2 = x(x + -3) + -6(x + -2)

Combine like terms: 6 + -6 = 0
0 + -5x + -3x + x2 = x(x + -3) + -6(x + -2)
-5x + -3x + x2 = x(x + -3) + -6(x + -2)

Combine like terms: -5x + -3x = -8x
-8x + x2 = x(x + -3) + -6(x + -2)

Reorder the terms:
-8x + x2 = x(-3 + x) + -6(x + -2)
-8x + x2 = (-3 * x + x * x) + -6(x + -2)
-8x + x2 = (-3x + x2) + -6(x + -2)

Reorder the terms:
-8x + x2 = -3x + x2 + -6(-2 + x)
-8x + x2 = -3x + x2 + (-2 * -6 + x * -6)
-8x + x2 = -3x + x2 + (12 + -6x)

Reorder the terms:
-8x + x2 = 12 + -3x + -6x + x2

Combine like terms: -3x + -6x = -9x
-8x + x2 = 12 + -9x + x2

Add '-1x2' to each side of the equation.
-8x + x2 + -1x2 = 12 + -9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8x + 0 = 12 + -9x + x2 + -1x2
-8x = 12 + -9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8x = 12 + -9x + 0
-8x = 12 + -9x

Solving
-8x = 12 + -9x

Solving for variable 'x'.

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

Add '9x' to each side of the equation.
-8x + 9x = 12 + -9x + 9x

Combine like terms: -8x + 9x = 1x
1x = 12 + -9x + 9x

Combine like terms: -9x + 9x = 0
1x = 12 + 0
1x = 12

Divide each side by '1'.
x = 12

Simplifying
x = 12

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