(x+3)(x+8)=(x+9)(x+4)

Solution for (x+3)(x+8)=(x+9)(x+4) equation:

Simplifying
(x + 3)(x + 8) = (x + 9)(x + 4)

Reorder the terms:
(3 + x)(x + 8) = (x + 9)(x + 4)

Reorder the terms:
(3 + x)(8 + x) = (x + 9)(x + 4)

Multiply (3 + x) * (8 + x)
(3(8 + x) + x(8 + x)) = (x + 9)(x + 4)
((8 * 3 + x * 3) + x(8 + x)) = (x + 9)(x + 4)
((24 + 3x) + x(8 + x)) = (x + 9)(x + 4)
(24 + 3x + (8 * x + x * x)) = (x + 9)(x + 4)
(24 + 3x + (8x + x2)) = (x + 9)(x + 4)

Combine like terms: 3x + 8x = 11x
(24 + 11x + x2) = (x + 9)(x + 4)

Reorder the terms:
24 + 11x + x2 = (9 + x)(x + 4)

Reorder the terms:
24 + 11x + x2 = (9 + x)(4 + x)

Multiply (9 + x) * (4 + x)
24 + 11x + x2 = (9(4 + x) + x(4 + x))
24 + 11x + x2 = ((4 * 9 + x * 9) + x(4 + x))
24 + 11x + x2 = ((36 + 9x) + x(4 + x))
24 + 11x + x2 = (36 + 9x + (4 * x + x * x))
24 + 11x + x2 = (36 + 9x + (4x + x2))

Combine like terms: 9x + 4x = 13x
24 + 11x + x2 = (36 + 13x + x2)

Add '-1x2' to each side of the equation.
24 + 11x + x2 + -1x2 = 36 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 11x + 0 = 36 + 13x + x2 + -1x2
24 + 11x = 36 + 13x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 11x = 36 + 13x + 0
24 + 11x = 36 + 13x

Solving
24 + 11x = 36 + 13x

Solving for variable 'x'.

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

Add '-13x' to each side of the equation.
24 + 11x + -13x = 36 + 13x + -13x

Combine like terms: 11x + -13x = -2x
24 + -2x = 36 + 13x + -13x

Combine like terms: 13x + -13x = 0
24 + -2x = 36 + 0
24 + -2x = 36

Add '-24' to each side of the equation.
24 + -24 + -2x = 36 + -24

Combine like terms: 24 + -24 = 0
0 + -2x = 36 + -24
-2x = 36 + -24

Combine like terms: 36 + -24 = 12
-2x = 12

Divide each side by '-2'.
x = -6

Simplifying
x = -6