(X-2)(x-3)=(x-7)(x+3)

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Solution for (X-2)(x-3)=(x-7)(x+3) equation: 


Simplifying
(X + -2)(x + -3) = (x + -7)(x + 3)

Reorder the terms:
(-2 + X)(x + -3) = (x + -7)(x + 3)

Reorder the terms:
(-2 + X)(-3 + x) = (x + -7)(x + 3)

Multiply (-2 + X) * (-3 + x)
(-2(-3 + x) + X(-3 + x)) = (x + -7)(x + 3)
((-3 * -2 + x * -2) + X(-3 + x)) = (x + -7)(x + 3)
((6 + -2x) + X(-3 + x)) = (x + -7)(x + 3)
(6 + -2x + (-3 * X + x * X)) = (x + -7)(x + 3)
(6 + -2x + (-3X + xX)) = (x + -7)(x + 3)

Reorder the terms:
(6 + -3X + -2x + xX) = (x + -7)(x + 3)
(6 + -3X + -2x + xX) = (x + -7)(x + 3)

Reorder the terms:
6 + -3X + -2x + xX = (-7 + x)(x + 3)

Reorder the terms:
6 + -3X + -2x + xX = (-7 + x)(3 + x)

Multiply (-7 + x) * (3 + x)
6 + -3X + -2x + xX = (-7(3 + x) + x(3 + x))
6 + -3X + -2x + xX = ((3 * -7 + x * -7) + x(3 + x))
6 + -3X + -2x + xX = ((-21 + -7x) + x(3 + x))
6 + -3X + -2x + xX = (-21 + -7x + (3 * x + x * x))
6 + -3X + -2x + xX = (-21 + -7x + (3x + x2))

Combine like terms: -7x + 3x = -4x
6 + -3X + -2x + xX = (-21 + -4x + x2)

Solving
6 + -3X + -2x + xX = -21 + -4x + 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 = -21 + -4x + -6 + x2

Reorder the terms:
6 + -6 + -3X + -2x + xX = -21 + -4x + -6 + x2

Combine like terms: 6 + -6 = 0
0 + -3X + -2x + xX = -21 + -4x + -6 + x2
-3X + -2x + xX = -21 + -4x + -6 + x2

Reorder the terms:
-3X + -2x + xX = -21 + -6 + -4x + x2

Combine like terms: -21 + -6 = -27
-3X + -2x + xX = -27 + -4x + x2

Add '2x' to each side of the equation.
-3X + -2x + 2x + xX = -27 + -4x + 2x + x2

Combine like terms: -2x + 2x = 0
-3X + 0 + xX = -27 + -4x + 2x + x2
-3X + xX = -27 + -4x + 2x + x2

Combine like terms: -4x + 2x = -2x
-3X + xX = -27 + -2x + x2

Reorder the terms:
27 + -3X + 2x + xX + -1x2 = -27 + -2x + x2 + 27 + 2x + -1x2

Reorder the terms:
27 + -3X + 2x + xX + -1x2 = -27 + 27 + -2x + 2x + x2 + -1x2

Combine like terms: -27 + 27 = 0
27 + -3X + 2x + xX + -1x2 = 0 + -2x + 2x + x2 + -1x2
27 + -3X + 2x + xX + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
27 + -3X + 2x + xX + -1x2 = 0 + x2 + -1x2
27 + -3X + 2x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
27 + -3X + 2x + xX + -1x2 = 0

The solution to this equation could not be determined.

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