(X-3)(x+4)-(x-3)(x-8)=0

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Solution for (X-3)(x+4)-(x-3)(x-8)=0 equation: 


Simplifying
(X + -3)(x + 4) + -1(x + -3)(x + -8) = 0

Reorder the terms:
(-3 + X)(x + 4) + -1(x + -3)(x + -8) = 0

Reorder the terms:
(-3 + X)(4 + x) + -1(x + -3)(x + -8) = 0

Multiply (-3 + X) * (4 + x)
(-3(4 + x) + X(4 + x)) + -1(x + -3)(x + -8) = 0
((4 * -3 + x * -3) + X(4 + x)) + -1(x + -3)(x + -8) = 0
((-12 + -3x) + X(4 + x)) + -1(x + -3)(x + -8) = 0
(-12 + -3x + (4 * X + x * X)) + -1(x + -3)(x + -8) = 0
(-12 + -3x + (4X + xX)) + -1(x + -3)(x + -8) = 0

Reorder the terms:
(-12 + 4X + -3x + xX) + -1(x + -3)(x + -8) = 0
(-12 + 4X + -3x + xX) + -1(x + -3)(x + -8) = 0

Reorder the terms:
-12 + 4X + -3x + xX + -1(-3 + x)(x + -8) = 0

Reorder the terms:
-12 + 4X + -3x + xX + -1(-3 + x)(-8 + x) = 0

Multiply (-3 + x) * (-8 + x)
-12 + 4X + -3x + xX + -1(-3(-8 + x) + x(-8 + x)) = 0
-12 + 4X + -3x + xX + -1((-8 * -3 + x * -3) + x(-8 + x)) = 0
-12 + 4X + -3x + xX + -1((24 + -3x) + x(-8 + x)) = 0
-12 + 4X + -3x + xX + -1(24 + -3x + (-8 * x + x * x)) = 0
-12 + 4X + -3x + xX + -1(24 + -3x + (-8x + x2)) = 0

Combine like terms: -3x + -8x = -11x
-12 + 4X + -3x + xX + -1(24 + -11x + x2) = 0
-12 + 4X + -3x + xX + (24 * -1 + -11x * -1 + x2 * -1) = 0
-12 + 4X + -3x + xX + (-24 + 11x + -1x2) = 0

Reorder the terms:
-12 + -24 + 4X + -3x + 11x + xX + -1x2 = 0

Combine like terms: -12 + -24 = -36
-36 + 4X + -3x + 11x + xX + -1x2 = 0

Combine like terms: -3x + 11x = 8x
-36 + 4X + 8x + xX + -1x2 = 0

Solving
-36 + 4X + 8x + xX + -1x2 = 0

Solving for variable 'X'.

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

Add '36' to each side of the equation.
-36 + 4X + 8x + xX + 36 + -1x2 = 0 + 36

Reorder the terms:
-36 + 36 + 4X + 8x + xX + -1x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 4X + 8x + xX + -1x2 = 0 + 36
4X + 8x + xX + -1x2 = 0 + 36

Combine like terms: 0 + 36 = 36
4X + 8x + xX + -1x2 = 36

Add '-8x' to each side of the equation.
4X + 8x + xX + -8x + -1x2 = 36 + -8x

Reorder the terms:
4X + 8x + -8x + xX + -1x2 = 36 + -8x

Combine like terms: 8x + -8x = 0
4X + 0 + xX + -1x2 = 36 + -8x
4X + xX + -1x2 = 36 + -8x

Add 'x2' to each side of the equation.
4X + xX + -1x2 + x2 = 36 + -8x + x2

Combine like terms: -1x2 + x2 = 0
4X + xX + 0 = 36 + -8x + x2
4X + xX = 36 + -8x + x2

Reorder the terms:
-36 + 4X + 8x + xX + -1x2 = 36 + -8x + x2 + -36 + 8x + -1x2

Reorder the terms:
-36 + 4X + 8x + xX + -1x2 = 36 + -36 + -8x + 8x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-36 + 4X + 8x + xX + -1x2 = 0 + -8x + 8x + x2 + -1x2
-36 + 4X + 8x + xX + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-36 + 4X + 8x + xX + -1x2 = 0 + x2 + -1x2
-36 + 4X + 8x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + 4X + 8x + xX + -1x2 = 0

The solution to this equation could not be determined.

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