(x+1)(x+8)=(x+3)(x+5)

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Solution for (x+1)(x+8)=(x+3)(x+5) equation:


Simplifying
(x + 1)(x + 8) = (x + 3)(x + 5)

Reorder the terms:
(1 + x)(x + 8) = (x + 3)(x + 5)

Reorder the terms:
(1 + x)(8 + x) = (x + 3)(x + 5)

Multiply (1 + x) * (8 + x)
(1(8 + x) + x(8 + x)) = (x + 3)(x + 5)
((8 * 1 + x * 1) + x(8 + x)) = (x + 3)(x + 5)
((8 + 1x) + x(8 + x)) = (x + 3)(x + 5)
(8 + 1x + (8 * x + x * x)) = (x + 3)(x + 5)
(8 + 1x + (8x + x2)) = (x + 3)(x + 5)

Combine like terms: 1x + 8x = 9x
(8 + 9x + x2) = (x + 3)(x + 5)

Reorder the terms:
8 + 9x + x2 = (3 + x)(x + 5)

Reorder the terms:
8 + 9x + x2 = (3 + x)(5 + x)

Multiply (3 + x) * (5 + x)
8 + 9x + x2 = (3(5 + x) + x(5 + x))
8 + 9x + x2 = ((5 * 3 + x * 3) + x(5 + x))
8 + 9x + x2 = ((15 + 3x) + x(5 + x))
8 + 9x + x2 = (15 + 3x + (5 * x + x * x))
8 + 9x + x2 = (15 + 3x + (5x + x2))

Combine like terms: 3x + 5x = 8x
8 + 9x + x2 = (15 + 8x + x2)

Add '-1x2' to each side of the equation.
8 + 9x + x2 + -1x2 = 15 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 9x + 0 = 15 + 8x + x2 + -1x2
8 + 9x = 15 + 8x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 9x = 15 + 8x + 0
8 + 9x = 15 + 8x

Solving
8 + 9x = 15 + 8x

Solving for variable 'x'.

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

Add '-8x' to each side of the equation.
8 + 9x + -8x = 15 + 8x + -8x

Combine like terms: 9x + -8x = 1x
8 + 1x = 15 + 8x + -8x

Combine like terms: 8x + -8x = 0
8 + 1x = 15 + 0
8 + 1x = 15

Add '-8' to each side of the equation.
8 + -8 + 1x = 15 + -8

Combine like terms: 8 + -8 = 0
0 + 1x = 15 + -8
1x = 15 + -8

Combine like terms: 15 + -8 = 7
1x = 7

Divide each side by '1'.
x = 7

Simplifying
x = 7

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