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

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


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

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

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

Multiply (7 + x) * (2 + x)
(7(2 + x) + x(2 + x)) = (x + 1)(x + 1)
((2 * 7 + x * 7) + x(2 + x)) = (x + 1)(x + 1)
((14 + 7x) + x(2 + x)) = (x + 1)(x + 1)
(14 + 7x + (2 * x + x * x)) = (x + 1)(x + 1)
(14 + 7x + (2x + x2)) = (x + 1)(x + 1)

Combine like terms: 7x + 2x = 9x
(14 + 9x + x2) = (x + 1)(x + 1)

Reorder the terms:
14 + 9x + x2 = (1 + x)(x + 1)

Reorder the terms:
14 + 9x + x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
14 + 9x + x2 = (1(1 + x) + x(1 + x))
14 + 9x + x2 = ((1 * 1 + x * 1) + x(1 + x))
14 + 9x + x2 = ((1 + 1x) + x(1 + x))
14 + 9x + x2 = (1 + 1x + (1 * x + x * x))
14 + 9x + x2 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
14 + 9x + x2 = (1 + 2x + x2)

Add '-1x2' to each side of the equation.
14 + 9x + x2 + -1x2 = 1 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + 9x + 0 = 1 + 2x + x2 + -1x2
14 + 9x = 1 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + 9x = 1 + 2x + 0
14 + 9x = 1 + 2x

Solving
14 + 9x = 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.
14 + 9x + -2x = 1 + 2x + -2x

Combine like terms: 9x + -2x = 7x
14 + 7x = 1 + 2x + -2x

Combine like terms: 2x + -2x = 0
14 + 7x = 1 + 0
14 + 7x = 1

Add '-14' to each side of the equation.
14 + -14 + 7x = 1 + -14

Combine like terms: 14 + -14 = 0
0 + 7x = 1 + -14
7x = 1 + -14

Combine like terms: 1 + -14 = -13
7x = -13

Divide each side by '7'.
x = -1.857142857

Simplifying
x = -1.857142857

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