((x+1)(x+18))-10x=0

Solution for ((x+1)(x+18))-10x=0 equation:

Simplifying
((x + 1)(x + 18)) + -10x = 0

Reorder the terms:
((1 + x)(x + 18)) + -10x = 0

Reorder the terms:
((1 + x)(18 + x)) + -10x = 0

Multiply (1 + x) * (18 + x)
((1(18 + x) + x(18 + x))) + -10x = 0
(((18 * 1 + x * 1) + x(18 + x))) + -10x = 0
(((18 + 1x) + x(18 + x))) + -10x = 0
((18 + 1x + (18 * x + x * x))) + -10x = 0
((18 + 1x + (18x + x2))) + -10x = 0

Combine like terms: 1x + 18x = 19x
((18 + 19x + x2)) + -10x = 0
(18 + 19x + x2) + -10x = 0

Remove parenthesis around (18 + 19x + x2)
18 + 19x + x2 + -10x = 0

Reorder the terms:
18 + 19x + -10x + x2 = 0

Combine like terms: 19x + -10x = 9x
18 + 9x + x2 = 0

Solving
18 + 9x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(3 + 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-6, -3}