(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 = -6x
(-7 + -6x + x2) = (x + -1)(x + -3)

Reorder the terms:
-7 + -6x + x2 = (-1 + x)(x + -3)

Reorder the terms:
-7 + -6x + x2 = (-1 + x)(-3 + x)

Multiply (-1 + x) * (-3 + x)
-7 + -6x + x2 = (-1(-3 + x) + x(-3 + x))
-7 + -6x + x2 = ((-3 * -1 + x * -1) + x(-3 + x))
-7 + -6x + x2 = ((3 + -1x) + x(-3 + x))
-7 + -6x + x2 = (3 + -1x + (-3 * x + x * x))
-7 + -6x + x2 = (3 + -1x + (-3x + x2))

Combine like terms: -1x + -3x = -4x
-7 + -6x + x2 = (3 + -4x + x2)

Add '-1x2' to each side of the equation.
-7 + -6x + x2 + -1x2 = 3 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + -6x + 0 = 3 + -4x + x2 + -1x2
-7 + -6x = 3 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + -6x = 3 + -4x + 0
-7 + -6x = 3 + -4x

Solving
-7 + -6x = 3 + -4x

Solving for variable 'x'.

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

Add '4x' to each side of the equation.
-7 + -6x + 4x = 3 + -4x + 4x

Combine like terms: -6x + 4x = -2x
-7 + -2x = 3 + -4x + 4x

Combine like terms: -4x + 4x = 0
-7 + -2x = 3 + 0
-7 + -2x = 3

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

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

Combine like terms: 3 + 7 = 10
-2x = 10

Divide each side by '-2'.
x = -5

Simplifying
x = -5

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