(x+6)(x+17)=0

Solution for (x+6)(x+17)=0 equation:

Simplifying
(x + 6)(x + 17) = 0

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

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

Multiply (6 + x) * (17 + x)
(6(17 + x) + x(17 + x)) = 0
((17 * 6 + x * 6) + x(17 + x)) = 0
((102 + 6x) + x(17 + x)) = 0
(102 + 6x + (17 * x + x * x)) = 0
(102 + 6x + (17x + x2)) = 0

Combine like terms: 6x + 17x = 23x
(102 + 23x + x2) = 0

Solving
102 + 23x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(17 + x)(6 + 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 '(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
Solution
x = {-17, -6}