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

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


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

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

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

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

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

Reorder the terms:
-7 + 6x + x2 = (1 + x)(x + 1)

Reorder the terms:
-7 + 6x + x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
-7 + 6x + x2 = (1(1 + x) + x(1 + x))
-7 + 6x + x2 = ((1 * 1 + x * 1) + x(1 + x))
-7 + 6x + x2 = ((1 + 1x) + x(1 + x))
-7 + 6x + x2 = (1 + 1x + (1 * x + x * x))
-7 + 6x + x2 = (1 + 1x + (1x + x2))

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

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

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

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

Solving
-7 + 6x = 1 + 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 = 1 + 2x + -2x

Combine like terms: 6x + -2x = 4x
-7 + 4x = 1 + 2x + -2x

Combine like terms: 2x + -2x = 0
-7 + 4x = 1 + 0
-7 + 4x = 1

Add '7' to each side of the equation.
-7 + 7 + 4x = 1 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 1 + 7
4x = 1 + 7

Combine like terms: 1 + 7 = 8
4x = 8

Divide each side by '4'.
x = 2

Simplifying
x = 2

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