(x+1)(x+8)=(x+2)(x+3)

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Solution for (x+1)(x+8)=(x+2)(x+3) equation:


Simplifying
(x + 1)(x + 8) = (x + 2)(x + 3)

Reorder the terms:
(1 + x)(x + 8) = (x + 2)(x + 3)

Reorder the terms:
(1 + x)(8 + x) = (x + 2)(x + 3)

Multiply (1 + x) * (8 + x)
(1(8 + x) + x(8 + x)) = (x + 2)(x + 3)
((8 * 1 + x * 1) + x(8 + x)) = (x + 2)(x + 3)
((8 + 1x) + x(8 + x)) = (x + 2)(x + 3)
(8 + 1x + (8 * x + x * x)) = (x + 2)(x + 3)
(8 + 1x + (8x + x2)) = (x + 2)(x + 3)

Combine like terms: 1x + 8x = 9x
(8 + 9x + x2) = (x + 2)(x + 3)

Reorder the terms:
8 + 9x + x2 = (2 + x)(x + 3)

Reorder the terms:
8 + 9x + x2 = (2 + x)(3 + x)

Multiply (2 + x) * (3 + x)
8 + 9x + x2 = (2(3 + x) + x(3 + x))
8 + 9x + x2 = ((3 * 2 + x * 2) + x(3 + x))
8 + 9x + x2 = ((6 + 2x) + x(3 + x))
8 + 9x + x2 = (6 + 2x + (3 * x + x * x))
8 + 9x + x2 = (6 + 2x + (3x + x2))

Combine like terms: 2x + 3x = 5x
8 + 9x + x2 = (6 + 5x + x2)

Add '-1x2' to each side of the equation.
8 + 9x + x2 + -1x2 = 6 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 9x + 0 = 6 + 5x + x2 + -1x2
8 + 9x = 6 + 5x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 9x = 6 + 5x + 0
8 + 9x = 6 + 5x

Solving
8 + 9x = 6 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
8 + 9x + -5x = 6 + 5x + -5x

Combine like terms: 9x + -5x = 4x
8 + 4x = 6 + 5x + -5x

Combine like terms: 5x + -5x = 0
8 + 4x = 6 + 0
8 + 4x = 6

Add '-8' to each side of the equation.
8 + -8 + 4x = 6 + -8

Combine like terms: 8 + -8 = 0
0 + 4x = 6 + -8
4x = 6 + -8

Combine like terms: 6 + -8 = -2
4x = -2

Divide each side by '4'.
x = -0.5

Simplifying
x = -0.5

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