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

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

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

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

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

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

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2) = (x + -5)(x + -1)

Reorder the terms:
3 + 4x + x2 = (-5 + x)(x + -1)

Reorder the terms:
3 + 4x + x2 = (-5 + x)(-1 + x)

Multiply (-5 + x) * (-1 + x)
3 + 4x + x2 = (-5(-1 + x) + x(-1 + x))
3 + 4x + x2 = ((-1 * -5 + x * -5) + x(-1 + x))
3 + 4x + x2 = ((5 + -5x) + x(-1 + x))
3 + 4x + x2 = (5 + -5x + (-1 * x + x * x))
3 + 4x + x2 = (5 + -5x + (-1x + x2))

Combine like terms: -5x + -1x = -6x
3 + 4x + x2 = (5 + -6x + x2)

Add '-1x2' to each side of the equation.
3 + 4x + x2 + -1x2 = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 4x + 0 = 5 + -6x + x2 + -1x2
3 + 4x = 5 + -6x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 4x = 5 + -6x + 0
3 + 4x = 5 + -6x

Solving
3 + 4x = 5 + -6x

Solving for variable 'x'.

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

Add '6x' to each side of the equation.
3 + 4x + 6x = 5 + -6x + 6x

Combine like terms: 4x + 6x = 10x
3 + 10x = 5 + -6x + 6x

Combine like terms: -6x + 6x = 0
3 + 10x = 5 + 0
3 + 10x = 5

Add '-3' to each side of the equation.
3 + -3 + 10x = 5 + -3

Combine like terms: 3 + -3 = 0
0 + 10x = 5 + -3
10x = 5 + -3

Combine like terms: 5 + -3 = 2
10x = 2

Divide each side by '10'.
x = 0.2

Simplifying
x = 0.2