(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 = 3x
(2 + 3x + x2) = (x + -1)(x + 7)

Reorder the terms:
2 + 3x + x2 = (-1 + x)(x + 7)

Reorder the terms:
2 + 3x + x2 = (-1 + x)(7 + x)

Multiply (-1 + x) * (7 + x)
2 + 3x + x2 = (-1(7 + x) + x(7 + x))
2 + 3x + x2 = ((7 * -1 + x * -1) + x(7 + x))
2 + 3x + x2 = ((-7 + -1x) + x(7 + x))
2 + 3x + x2 = (-7 + -1x + (7 * x + x * x))
2 + 3x + x2 = (-7 + -1x + (7x + x2))

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

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

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

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

Solving
2 + 3x = -7 + 6x

Solving for variable 'x'.

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

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

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

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

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

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

Combine like terms: -7 + -2 = -9
-3x = -9

Divide each side by '-3'.
x = 3

Simplifying
x = 3

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