(x+3)(x+8)=x

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

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

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

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

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

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

Solving
24 + 11x + x2 = x

Solving for variable 'x'.

Reorder the terms:
24 + 11x + -1x + x2 = x + -1x

Combine like terms: 11x + -1x = 10x
24 + 10x + x2 = x + -1x

Combine like terms: x + -1x = 0
24 + 10x + x2 = 0

Factor a trinomial.
(6 + x)(4 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

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

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

Simplifying
x = -6
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {-6, -4}