(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 = -2x
-7 + 6x + x2 = (-3 + -2x + x2)

Add '-1x2' to each side of the equation.
-7 + 6x + x2 + -1x2 = -3 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + 6x + 0 = -3 + -2x + x2 + -1x2
-7 + 6x = -3 + -2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + 6x = -3 + -2x + 0
-7 + 6x = -3 + -2x

Solving
-7 + 6x = -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 + 6x + 2x = -3 + -2x + 2x

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

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

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

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

Combine like terms: -3 + 7 = 4
8x = 4

Divide each side by '8'.
x = 0.5

Simplifying
x = 0.5

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