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

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


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

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

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

Multiply (-5 + X) * (-3 + x)
(-5(-3 + x) + X(-3 + x)) = (x + 3)(x + 7)
((-3 * -5 + x * -5) + X(-3 + x)) = (x + 3)(x + 7)
((15 + -5x) + X(-3 + x)) = (x + 3)(x + 7)
(15 + -5x + (-3 * X + x * X)) = (x + 3)(x + 7)
(15 + -5x + (-3X + xX)) = (x + 3)(x + 7)

Reorder the terms:
(15 + -3X + -5x + xX) = (x + 3)(x + 7)
(15 + -3X + -5x + xX) = (x + 3)(x + 7)

Reorder the terms:
15 + -3X + -5x + xX = (3 + x)(x + 7)

Reorder the terms:
15 + -3X + -5x + xX = (3 + x)(7 + x)

Multiply (3 + x) * (7 + x)
15 + -3X + -5x + xX = (3(7 + x) + x(7 + x))
15 + -3X + -5x + xX = ((7 * 3 + x * 3) + x(7 + x))
15 + -3X + -5x + xX = ((21 + 3x) + x(7 + x))
15 + -3X + -5x + xX = (21 + 3x + (7 * x + x * x))
15 + -3X + -5x + xX = (21 + 3x + (7x + x2))

Combine like terms: 3x + 7x = 10x
15 + -3X + -5x + xX = (21 + 10x + x2)

Solving
15 + -3X + -5x + xX = 21 + 10x + x2

Solving for variable 'X'.

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

Add '-15' to each side of the equation.
15 + -3X + -5x + -15 + xX = 21 + 10x + -15 + x2

Reorder the terms:
15 + -15 + -3X + -5x + xX = 21 + 10x + -15 + x2

Combine like terms: 15 + -15 = 0
0 + -3X + -5x + xX = 21 + 10x + -15 + x2
-3X + -5x + xX = 21 + 10x + -15 + x2

Reorder the terms:
-3X + -5x + xX = 21 + -15 + 10x + x2

Combine like terms: 21 + -15 = 6
-3X + -5x + xX = 6 + 10x + x2

Add '5x' to each side of the equation.
-3X + -5x + 5x + xX = 6 + 10x + 5x + x2

Combine like terms: -5x + 5x = 0
-3X + 0 + xX = 6 + 10x + 5x + x2
-3X + xX = 6 + 10x + 5x + x2

Combine like terms: 10x + 5x = 15x
-3X + xX = 6 + 15x + x2

Reorder the terms:
-6 + -3X + -15x + xX + -1x2 = 6 + 15x + x2 + -6 + -15x + -1x2

Reorder the terms:
-6 + -3X + -15x + xX + -1x2 = 6 + -6 + 15x + -15x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-6 + -3X + -15x + xX + -1x2 = 0 + 15x + -15x + x2 + -1x2
-6 + -3X + -15x + xX + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-6 + -3X + -15x + xX + -1x2 = 0 + x2 + -1x2
-6 + -3X + -15x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -3X + -15x + xX + -1x2 = 0

The solution to this equation could not be determined.

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