(x+7)(x+3)=(x+8)(x+1)

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Solution for (x+7)(x+3)=(x+8)(x+1) equation: 


Simplifying
(x + 7)(x + 3) = (x + 8)(x + 1)

Reorder the terms:
(7 + x)(x + 3) = (x + 8)(x + 1)

Reorder the terms:
(7 + x)(3 + x) = (x + 8)(x + 1)

Multiply (7 + x) * (3 + x)
(7(3 + x) + x(3 + x)) = (x + 8)(x + 1)
((3 * 7 + x * 7) + x(3 + x)) = (x + 8)(x + 1)
((21 + 7x) + x(3 + x)) = (x + 8)(x + 1)
(21 + 7x + (3 * x + x * x)) = (x + 8)(x + 1)
(21 + 7x + (3x + x2)) = (x + 8)(x + 1)

Combine like terms: 7x + 3x = 10x
(21 + 10x + x2) = (x + 8)(x + 1)

Reorder the terms:
21 + 10x + x2 = (8 + x)(x + 1)

Reorder the terms:
21 + 10x + x2 = (8 + x)(1 + x)

Multiply (8 + x) * (1 + x)
21 + 10x + x2 = (8(1 + x) + x(1 + x))
21 + 10x + x2 = ((1 * 8 + x * 8) + x(1 + x))
21 + 10x + x2 = ((8 + 8x) + x(1 + x))
21 + 10x + x2 = (8 + 8x + (1 * x + x * x))
21 + 10x + x2 = (8 + 8x + (1x + x2))

Combine like terms: 8x + 1x = 9x
21 + 10x + x2 = (8 + 9x + x2)

Add '-1x2' to each side of the equation.
21 + 10x + x2 + -1x2 = 8 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 10x + 0 = 8 + 9x + x2 + -1x2
21 + 10x = 8 + 9x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
21 + 10x = 8 + 9x + 0
21 + 10x = 8 + 9x

Solving
21 + 10x = 8 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
21 + 10x + -9x = 8 + 9x + -9x

Combine like terms: 10x + -9x = 1x
21 + 1x = 8 + 9x + -9x

Combine like terms: 9x + -9x = 0
21 + 1x = 8 + 0
21 + 1x = 8

Add '-21' to each side of the equation.
21 + -21 + 1x = 8 + -21

Combine like terms: 21 + -21 = 0
0 + 1x = 8 + -21
1x = 8 + -21

Combine like terms: 8 + -21 = -13
1x = -13

Divide each side by '1'.
x = -13

Simplifying
x = -13

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