(x-3)(x+7)-(X+1)(x+5)=0

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Solution for (x-3)(x+7)-(X+1)(x+5)=0 equation: 


Simplifying
(x + -3)(x + 7) + -1(X + 1)(x + 5) = 0

Reorder the terms:
(-3 + x)(x + 7) + -1(X + 1)(x + 5) = 0

Reorder the terms:
(-3 + x)(7 + x) + -1(X + 1)(x + 5) = 0

Multiply (-3 + x) * (7 + x)
(-3(7 + x) + x(7 + x)) + -1(X + 1)(x + 5) = 0
((7 * -3 + x * -3) + x(7 + x)) + -1(X + 1)(x + 5) = 0
((-21 + -3x) + x(7 + x)) + -1(X + 1)(x + 5) = 0
(-21 + -3x + (7 * x + x * x)) + -1(X + 1)(x + 5) = 0
(-21 + -3x + (7x + x2)) + -1(X + 1)(x + 5) = 0

Combine like terms: -3x + 7x = 4x
(-21 + 4x + x2) + -1(X + 1)(x + 5) = 0

Reorder the terms:
-21 + 4x + x2 + -1(1 + X)(x + 5) = 0

Reorder the terms:
-21 + 4x + x2 + -1(1 + X)(5 + x) = 0

Multiply (1 + X) * (5 + x)
-21 + 4x + x2 + -1(1(5 + x) + X(5 + x)) = 0
-21 + 4x + x2 + -1((5 * 1 + x * 1) + X(5 + x)) = 0
-21 + 4x + x2 + -1((5 + 1x) + X(5 + x)) = 0
-21 + 4x + x2 + -1(5 + 1x + (5 * X + x * X)) = 0
-21 + 4x + x2 + -1(5 + 1x + (5X + xX)) = 0

Reorder the terms:
-21 + 4x + x2 + -1(5 + 5X + 1x + xX) = 0
-21 + 4x + x2 + -1(5 + 5X + 1x + xX) = 0
-21 + 4x + x2 + (5 * -1 + 5X * -1 + 1x * -1 + xX * -1) = 0
-21 + 4x + x2 + (-5 + -5X + -1x + -1xX) = 0

Reorder the terms:
-21 + -5 + -5X + 4x + -1x + -1xX + x2 = 0

Combine like terms: -21 + -5 = -26
-26 + -5X + 4x + -1x + -1xX + x2 = 0

Combine like terms: 4x + -1x = 3x
-26 + -5X + 3x + -1xX + x2 = 0

Solving
-26 + -5X + 3x + -1xX + x2 = 0

Solving for variable 'X'.

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

Add '26' to each side of the equation.
-26 + -5X + 3x + -1xX + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -5X + 3x + -1xX + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -5X + 3x + -1xX + x2 = 0 + 26
-5X + 3x + -1xX + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-5X + 3x + -1xX + x2 = 26

Add '-3x' to each side of the equation.
-5X + 3x + -1xX + -3x + x2 = 26 + -3x

Reorder the terms:
-5X + 3x + -3x + -1xX + x2 = 26 + -3x

Combine like terms: 3x + -3x = 0
-5X + 0 + -1xX + x2 = 26 + -3x
-5X + -1xX + x2 = 26 + -3x

Add '-1x2' to each side of the equation.
-5X + -1xX + x2 + -1x2 = 26 + -3x + -1x2

Combine like terms: x2 + -1x2 = 0
-5X + -1xX + 0 = 26 + -3x + -1x2
-5X + -1xX = 26 + -3x + -1x2

Reorder the terms:
-26 + -5X + 3x + -1xX + x2 = 26 + -3x + -1x2 + -26 + 3x + x2

Reorder the terms:
-26 + -5X + 3x + -1xX + x2 = 26 + -26 + -3x + 3x + -1x2 + x2

Combine like terms: 26 + -26 = 0
-26 + -5X + 3x + -1xX + x2 = 0 + -3x + 3x + -1x2 + x2
-26 + -5X + 3x + -1xX + x2 = -3x + 3x + -1x2 + x2

Combine like terms: -3x + 3x = 0
-26 + -5X + 3x + -1xX + x2 = 0 + -1x2 + x2
-26 + -5X + 3x + -1xX + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-26 + -5X + 3x + -1xX + x2 = 0

The solution to this equation could not be determined.

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