(x-2)(x+1)=(x-1)(x-7)

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Solution for (x-2)(x+1)=(x-1)(x-7) equation: 


Simplifying
(x + -2)(x + 1) = (x + -1)(x + -7)

Reorder the terms:
(-2 + x)(x + 1) = (x + -1)(x + -7)

Reorder the terms:
(-2 + x)(1 + x) = (x + -1)(x + -7)

Multiply (-2 + x) * (1 + x)
(-2(1 + x) + x(1 + x)) = (x + -1)(x + -7)
((1 * -2 + x * -2) + x(1 + x)) = (x + -1)(x + -7)
((-2 + -2x) + x(1 + x)) = (x + -1)(x + -7)
(-2 + -2x + (1 * x + x * x)) = (x + -1)(x + -7)
(-2 + -2x + (1x + x2)) = (x + -1)(x + -7)

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

Reorder the terms:
-2 + -1x + x2 = (-1 + x)(x + -7)

Reorder the terms:
-2 + -1x + x2 = (-1 + x)(-7 + x)

Multiply (-1 + x) * (-7 + x)
-2 + -1x + x2 = (-1(-7 + x) + x(-7 + x))
-2 + -1x + x2 = ((-7 * -1 + x * -1) + x(-7 + x))
-2 + -1x + x2 = ((7 + -1x) + x(-7 + x))
-2 + -1x + x2 = (7 + -1x + (-7 * x + x * x))
-2 + -1x + x2 = (7 + -1x + (-7x + x2))

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

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

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

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

Solving
-2 + -1x = 7 + -8x

Solving for variable 'x'.

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

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

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

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

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

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

Combine like terms: 7 + 2 = 9
7x = 9

Divide each side by '7'.
x = 1.285714286

Simplifying
x = 1.285714286

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