(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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