(x-3)(7-X)-3=(x+5)(4-x)

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Solution for (x-3)(7-X)-3=(x+5)(4-x) equation: 


Simplifying
(x + -3)(7 + -1X) + -3 = (x + 5)(4 + -1x)

Reorder the terms:
(-3 + x)(7 + -1X) + -3 = (x + 5)(4 + -1x)

Multiply (-3 + x) * (7 + -1X)
(-3(7 + -1X) + x(7 + -1X)) + -3 = (x + 5)(4 + -1x)
((7 * -3 + -1X * -3) + x(7 + -1X)) + -3 = (x + 5)(4 + -1x)
((-21 + 3X) + x(7 + -1X)) + -3 = (x + 5)(4 + -1x)
(-21 + 3X + (7 * x + -1X * x)) + -3 = (x + 5)(4 + -1x)
(-21 + 3X + (7x + -1xX)) + -3 = (x + 5)(4 + -1x)
(-21 + 3X + 7x + -1xX) + -3 = (x + 5)(4 + -1x)

Reorder the terms:
-21 + -3 + 3X + 7x + -1xX = (x + 5)(4 + -1x)

Combine like terms: -21 + -3 = -24
-24 + 3X + 7x + -1xX = (x + 5)(4 + -1x)

Reorder the terms:
-24 + 3X + 7x + -1xX = (5 + x)(4 + -1x)

Multiply (5 + x) * (4 + -1x)
-24 + 3X + 7x + -1xX = (5(4 + -1x) + x(4 + -1x))
-24 + 3X + 7x + -1xX = ((4 * 5 + -1x * 5) + x(4 + -1x))
-24 + 3X + 7x + -1xX = ((20 + -5x) + x(4 + -1x))
-24 + 3X + 7x + -1xX = (20 + -5x + (4 * x + -1x * x))
-24 + 3X + 7x + -1xX = (20 + -5x + (4x + -1x2))

Combine like terms: -5x + 4x = -1x
-24 + 3X + 7x + -1xX = (20 + -1x + -1x2)

Solving
-24 + 3X + 7x + -1xX = 20 + -1x + -1x2

Solving for variable 'X'.

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

Add '24' to each side of the equation.
-24 + 3X + 7x + 24 + -1xX = 20 + -1x + 24 + -1x2

Reorder the terms:
-24 + 24 + 3X + 7x + -1xX = 20 + -1x + 24 + -1x2

Combine like terms: -24 + 24 = 0
0 + 3X + 7x + -1xX = 20 + -1x + 24 + -1x2
3X + 7x + -1xX = 20 + -1x + 24 + -1x2

Reorder the terms:
3X + 7x + -1xX = 20 + 24 + -1x + -1x2

Combine like terms: 20 + 24 = 44
3X + 7x + -1xX = 44 + -1x + -1x2

Add '-7x' to each side of the equation.
3X + 7x + -7x + -1xX = 44 + -1x + -7x + -1x2

Combine like terms: 7x + -7x = 0
3X + 0 + -1xX = 44 + -1x + -7x + -1x2
3X + -1xX = 44 + -1x + -7x + -1x2

Combine like terms: -1x + -7x = -8x
3X + -1xX = 44 + -8x + -1x2

Reorder the terms:
-44 + 3X + 8x + -1xX + x2 = 44 + -8x + -1x2 + -44 + 8x + x2

Reorder the terms:
-44 + 3X + 8x + -1xX + x2 = 44 + -44 + -8x + 8x + -1x2 + x2

Combine like terms: 44 + -44 = 0
-44 + 3X + 8x + -1xX + x2 = 0 + -8x + 8x + -1x2 + x2
-44 + 3X + 8x + -1xX + x2 = -8x + 8x + -1x2 + x2

Combine like terms: -8x + 8x = 0
-44 + 3X + 8x + -1xX + x2 = 0 + -1x2 + x2
-44 + 3X + 8x + -1xX + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-44 + 3X + 8x + -1xX + x2 = 0

The solution to this equation could not be determined.

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