(x+1)(x+17)=0

Solution for (x+1)(x+17)=0 equation:

Simplifying
(x + 1)(x + 17) = 0

Reorder the terms:
(1 + x)(x + 17) = 0

Reorder the terms:
(1 + x)(17 + x) = 0

Multiply (1 + x) * (17 + x)
(1(17 + x) + x(17 + x)) = 0
((17 * 1 + x * 1) + x(17 + x)) = 0
((17 + 1x) + x(17 + x)) = 0
(17 + 1x + (17 * x + x * x)) = 0
(17 + 1x + (17x + x2)) = 0

Combine like terms: 1x + 17x = 18x
(17 + 18x + x2) = 0

Solving
17 + 18x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(17 + x)(1 + x) = 0

Subproblem 1
Set the factor '(17 + x)' equal to zero and attempt to solve:

Simplifying
17 + x = 0

Solving
17 + x = 0

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

Add '-17' to each side of the equation.
17 + -17 + x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + x = 0 + -17
x = 0 + -17

Combine like terms: 0 + -17 = -17
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-17, -1}