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

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

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

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

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

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

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

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

Solving
-1 + 1X + -1x + xX = -5 + 5x

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 + -1x + 1 + xX = -5 + 1 + 5x

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

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

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

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

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

Combine like terms: 5x + x = 6x
1X + xX = -4 + 6x

Reorder the terms:
4 + 1X + -6x + xX = -4 + 6x + 4 + -6x

Reorder the terms:
4 + 1X + -6x + xX = -4 + 4 + 6x + -6x

Combine like terms: -4 + 4 = 0
4 + 1X + -6x + xX = 0 + 6x + -6x
4 + 1X + -6x + xX = 6x + -6x

Combine like terms: 6x + -6x = 0
4 + 1X + -6x + xX = 0

The solution to this equation could not be determined.