(x+1)(x+7)=(x-1)(x+3)

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Solution for (x+1)(x+7)=(x-1)(x+3) equation: 


Simplifying
(x + 1)(x + 7) = (x + -1)(x + 3)

Reorder the terms:
(1 + x)(x + 7) = (x + -1)(x + 3)

Reorder the terms:
(1 + x)(7 + x) = (x + -1)(x + 3)

Multiply (1 + x) * (7 + x)
(1(7 + x) + x(7 + x)) = (x + -1)(x + 3)
((7 * 1 + x * 1) + x(7 + x)) = (x + -1)(x + 3)
((7 + 1x) + x(7 + x)) = (x + -1)(x + 3)
(7 + 1x + (7 * x + x * x)) = (x + -1)(x + 3)
(7 + 1x + (7x + x2)) = (x + -1)(x + 3)

Combine like terms: 1x + 7x = 8x
(7 + 8x + x2) = (x + -1)(x + 3)

Reorder the terms:
7 + 8x + x2 = (-1 + x)(x + 3)

Reorder the terms:
7 + 8x + x2 = (-1 + x)(3 + x)

Multiply (-1 + x) * (3 + x)
7 + 8x + x2 = (-1(3 + x) + x(3 + x))
7 + 8x + x2 = ((3 * -1 + x * -1) + x(3 + x))
7 + 8x + x2 = ((-3 + -1x) + x(3 + x))
7 + 8x + x2 = (-3 + -1x + (3 * x + x * x))
7 + 8x + x2 = (-3 + -1x + (3x + x2))

Combine like terms: -1x + 3x = 2x
7 + 8x + x2 = (-3 + 2x + x2)

Add '-1x2' to each side of the equation.
7 + 8x + x2 + -1x2 = -3 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 8x + 0 = -3 + 2x + x2 + -1x2
7 + 8x = -3 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 8x = -3 + 2x + 0
7 + 8x = -3 + 2x

Solving
7 + 8x = -3 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
7 + 8x + -2x = -3 + 2x + -2x

Combine like terms: 8x + -2x = 6x
7 + 6x = -3 + 2x + -2x

Combine like terms: 2x + -2x = 0
7 + 6x = -3 + 0
7 + 6x = -3

Add '-7' to each side of the equation.
7 + -7 + 6x = -3 + -7

Combine like terms: 7 + -7 = 0
0 + 6x = -3 + -7
6x = -3 + -7

Combine like terms: -3 + -7 = -10
6x = -10

Divide each side by '6'.
x = -1.666666667

Simplifying
x = -1.666666667

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