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

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


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

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

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

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

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

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

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

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

Combine like terms: -3x + 3x = 0
2 + -3x + x2 = (-9 + 0 + x2)
2 + -3x + x2 = (-9 + x2)

Add '-1x2' to each side of the equation.
2 + -3x + x2 + -1x2 = -9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x + 0 = -9 + x2 + -1x2
2 + -3x = -9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x = -9 + 0
2 + -3x = -9

Solving
2 + -3x = -9

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + -3x = -9 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = -9 + -2
-3x = -9 + -2

Combine like terms: -9 + -2 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667

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