(X+2)(2x-6)=(x-3)(x-5)

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Solution for (X+2)(2x-6)=(x-3)(x-5) equation: 


Simplifying
(X + 2)(2x + -6) = (x + -3)(x + -5)

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

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

Multiply (2 + X) * (-6 + 2x)
(2(-6 + 2x) + X(-6 + 2x)) = (x + -3)(x + -5)
((-6 * 2 + 2x * 2) + X(-6 + 2x)) = (x + -3)(x + -5)
((-12 + 4x) + X(-6 + 2x)) = (x + -3)(x + -5)
(-12 + 4x + (-6 * X + 2x * X)) = (x + -3)(x + -5)
(-12 + 4x + (-6X + 2xX)) = (x + -3)(x + -5)

Reorder the terms:
(-12 + -6X + 4x + 2xX) = (x + -3)(x + -5)
(-12 + -6X + 4x + 2xX) = (x + -3)(x + -5)

Reorder the terms:
-12 + -6X + 4x + 2xX = (-3 + x)(x + -5)

Reorder the terms:
-12 + -6X + 4x + 2xX = (-3 + x)(-5 + x)

Multiply (-3 + x) * (-5 + x)
-12 + -6X + 4x + 2xX = (-3(-5 + x) + x(-5 + x))
-12 + -6X + 4x + 2xX = ((-5 * -3 + x * -3) + x(-5 + x))
-12 + -6X + 4x + 2xX = ((15 + -3x) + x(-5 + x))
-12 + -6X + 4x + 2xX = (15 + -3x + (-5 * x + x * x))
-12 + -6X + 4x + 2xX = (15 + -3x + (-5x + x2))

Combine like terms: -3x + -5x = -8x
-12 + -6X + 4x + 2xX = (15 + -8x + x2)

Solving
-12 + -6X + 4x + 2xX = 15 + -8x + x2

Solving for variable 'X'.

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

Add '12' to each side of the equation.
-12 + -6X + 4x + 12 + 2xX = 15 + -8x + 12 + x2

Reorder the terms:
-12 + 12 + -6X + 4x + 2xX = 15 + -8x + 12 + x2

Combine like terms: -12 + 12 = 0
0 + -6X + 4x + 2xX = 15 + -8x + 12 + x2
-6X + 4x + 2xX = 15 + -8x + 12 + x2

Reorder the terms:
-6X + 4x + 2xX = 15 + 12 + -8x + x2

Combine like terms: 15 + 12 = 27
-6X + 4x + 2xX = 27 + -8x + x2

Add '-4x' to each side of the equation.
-6X + 4x + -4x + 2xX = 27 + -8x + -4x + x2

Combine like terms: 4x + -4x = 0
-6X + 0 + 2xX = 27 + -8x + -4x + x2
-6X + 2xX = 27 + -8x + -4x + x2

Combine like terms: -8x + -4x = -12x
-6X + 2xX = 27 + -12x + x2

Reorder the terms:
-27 + -6X + 12x + 2xX + -1x2 = 27 + -12x + x2 + -27 + 12x + -1x2

Reorder the terms:
-27 + -6X + 12x + 2xX + -1x2 = 27 + -27 + -12x + 12x + x2 + -1x2

Combine like terms: 27 + -27 = 0
-27 + -6X + 12x + 2xX + -1x2 = 0 + -12x + 12x + x2 + -1x2
-27 + -6X + 12x + 2xX + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-27 + -6X + 12x + 2xX + -1x2 = 0 + x2 + -1x2
-27 + -6X + 12x + 2xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-27 + -6X + 12x + 2xX + -1x2 = 0

The solution to this equation could not be determined.

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