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

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


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

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

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

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

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

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

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

Multiply (-1 + x) * (-3 + 5x)
-1 + 1X + -3x + 3xX = (-1(-3 + 5x) + x(-3 + 5x))
-1 + 1X + -3x + 3xX = ((-3 * -1 + 5x * -1) + x(-3 + 5x))
-1 + 1X + -3x + 3xX = ((3 + -5x) + x(-3 + 5x))
-1 + 1X + -3x + 3xX = (3 + -5x + (-3 * x + 5x * x))
-1 + 1X + -3x + 3xX = (3 + -5x + (-3x + 5x2))

Combine like terms: -5x + -3x = -8x
-1 + 1X + -3x + 3xX = (3 + -8x + 5x2)

Solving
-1 + 1X + -3x + 3xX = 3 + -8x + 5x2

Solving for variable 'X'.

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

Add '1' to each side of the equation.
-1 + 1X + -3x + 1 + 3xX = 3 + -8x + 1 + 5x2

Reorder the terms:
-1 + 1 + 1X + -3x + 3xX = 3 + -8x + 1 + 5x2

Combine like terms: -1 + 1 = 0
0 + 1X + -3x + 3xX = 3 + -8x + 1 + 5x2
1X + -3x + 3xX = 3 + -8x + 1 + 5x2

Reorder the terms:
1X + -3x + 3xX = 3 + 1 + -8x + 5x2

Combine like terms: 3 + 1 = 4
1X + -3x + 3xX = 4 + -8x + 5x2

Add '3x' to each side of the equation.
1X + -3x + 3x + 3xX = 4 + -8x + 3x + 5x2

Combine like terms: -3x + 3x = 0
1X + 0 + 3xX = 4 + -8x + 3x + 5x2
1X + 3xX = 4 + -8x + 3x + 5x2

Combine like terms: -8x + 3x = -5x
1X + 3xX = 4 + -5x + 5x2

Reorder the terms:
-4 + 1X + 5x + 3xX + -5x2 = 4 + -5x + 5x2 + -4 + 5x + -5x2

Reorder the terms:
-4 + 1X + 5x + 3xX + -5x2 = 4 + -4 + -5x + 5x + 5x2 + -5x2

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

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

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

The solution to this equation could not be determined.

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