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

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


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

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

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

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

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

Reorder the terms:
7 + 8x + x2 = (1 + x)(x + 2)

Reorder the terms:
7 + 8x + x2 = (1 + x)(2 + x)

Multiply (1 + x) * (2 + x)
7 + 8x + x2 = (1(2 + x) + x(2 + x))
7 + 8x + x2 = ((2 * 1 + x * 1) + x(2 + x))
7 + 8x + x2 = ((2 + 1x) + x(2 + x))
7 + 8x + x2 = (2 + 1x + (2 * x + x * x))
7 + 8x + x2 = (2 + 1x + (2x + x2))

Combine like terms: 1x + 2x = 3x
7 + 8x + x2 = (2 + 3x + x2)

Add '-1x2' to each side of the equation.
7 + 8x + x2 + -1x2 = 2 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 8x + 0 = 2 + 3x + x2 + -1x2
7 + 8x = 2 + 3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 8x = 2 + 3x + 0
7 + 8x = 2 + 3x

Solving
7 + 8x = 2 + 3x

Solving for variable 'x'.

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

Add '-3x' to each side of the equation.
7 + 8x + -3x = 2 + 3x + -3x

Combine like terms: 8x + -3x = 5x
7 + 5x = 2 + 3x + -3x

Combine like terms: 3x + -3x = 0
7 + 5x = 2 + 0
7 + 5x = 2

Add '-7' to each side of the equation.
7 + -7 + 5x = 2 + -7

Combine like terms: 7 + -7 = 0
0 + 5x = 2 + -7
5x = 2 + -7

Combine like terms: 2 + -7 = -5
5x = -5

Divide each side by '5'.
x = -1

Simplifying
x = -1

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