(X-1)(x+3)=(2x-1)(x-1)

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Solution for (X-1)(x+3)=(2x-1)(x-1) equation: 


Simplifying
(X + -1)(x + 3) = (2x + -1)(x + -1)

Reorder the terms:
(-1 + X)(x + 3) = (2x + -1)(x + -1)

Reorder the terms:
(-1 + X)(3 + x) = (2x + -1)(x + -1)

Multiply (-1 + X) * (3 + x)
(-1(3 + x) + X(3 + x)) = (2x + -1)(x + -1)
((3 * -1 + x * -1) + X(3 + x)) = (2x + -1)(x + -1)
((-3 + -1x) + X(3 + x)) = (2x + -1)(x + -1)
(-3 + -1x + (3 * X + x * X)) = (2x + -1)(x + -1)
(-3 + -1x + (3X + xX)) = (2x + -1)(x + -1)

Reorder the terms:
(-3 + 3X + -1x + xX) = (2x + -1)(x + -1)
(-3 + 3X + -1x + xX) = (2x + -1)(x + -1)

Reorder the terms:
-3 + 3X + -1x + xX = (-1 + 2x)(x + -1)

Reorder the terms:
-3 + 3X + -1x + xX = (-1 + 2x)(-1 + x)

Multiply (-1 + 2x) * (-1 + x)
-3 + 3X + -1x + xX = (-1(-1 + x) + 2x * (-1 + x))
-3 + 3X + -1x + xX = ((-1 * -1 + x * -1) + 2x * (-1 + x))
-3 + 3X + -1x + xX = ((1 + -1x) + 2x * (-1 + x))
-3 + 3X + -1x + xX = (1 + -1x + (-1 * 2x + x * 2x))
-3 + 3X + -1x + xX = (1 + -1x + (-2x + 2x2))

Combine like terms: -1x + -2x = -3x
-3 + 3X + -1x + xX = (1 + -3x + 2x2)

Solving
-3 + 3X + -1x + xX = 1 + -3x + 2x2

Solving for variable 'X'.

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

Add '3' to each side of the equation.
-3 + 3X + -1x + 3 + xX = 1 + -3x + 3 + 2x2

Reorder the terms:
-3 + 3 + 3X + -1x + xX = 1 + -3x + 3 + 2x2

Combine like terms: -3 + 3 = 0
0 + 3X + -1x + xX = 1 + -3x + 3 + 2x2
3X + -1x + xX = 1 + -3x + 3 + 2x2

Reorder the terms:
3X + -1x + xX = 1 + 3 + -3x + 2x2

Combine like terms: 1 + 3 = 4
3X + -1x + xX = 4 + -3x + 2x2

Add 'x' to each side of the equation.
3X + -1x + x + xX = 4 + -3x + x + 2x2

Combine like terms: -1x + x = 0
3X + 0 + xX = 4 + -3x + x + 2x2
3X + xX = 4 + -3x + x + 2x2

Combine like terms: -3x + x = -2x
3X + xX = 4 + -2x + 2x2

Reorder the terms:
-4 + 3X + 2x + xX + -2x2 = 4 + -2x + 2x2 + -4 + 2x + -2x2

Reorder the terms:
-4 + 3X + 2x + xX + -2x2 = 4 + -4 + -2x + 2x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
-4 + 3X + 2x + xX + -2x2 = 0 + -2x + 2x + 2x2 + -2x2
-4 + 3X + 2x + xX + -2x2 = -2x + 2x + 2x2 + -2x2

Combine like terms: -2x + 2x = 0
-4 + 3X + 2x + xX + -2x2 = 0 + 2x2 + -2x2
-4 + 3X + 2x + xX + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 3X + 2x + xX + -2x2 = 0

The solution to this equation could not be determined.

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