(x+1)(x+18)=8x

Solution for (x+1)(x+18)=8x equation:

Simplifying
(x + 1)(x + 18) = 8x

Reorder the terms:
(1 + x)(x + 18) = 8x

Reorder the terms:
(1 + x)(18 + x) = 8x

Multiply (1 + x) * (18 + x)
(1(18 + x) + x(18 + x)) = 8x
((18 * 1 + x * 1) + x(18 + x)) = 8x
((18 + 1x) + x(18 + x)) = 8x
(18 + 1x + (18 * x + x * x)) = 8x
(18 + 1x + (18x + x2)) = 8x

Combine like terms: 1x + 18x = 19x
(18 + 19x + x2) = 8x

Solving
18 + 19x + x2 = 8x

Solving for variable 'x'.

Reorder the terms:
18 + 19x + -8x + x2 = 8x + -8x

Combine like terms: 19x + -8x = 11x
18 + 11x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
18 + 11x + x2 = 0

Factor a trinomial.
(9 + x)(2 + x) = 0

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-9, -2}