(x+3)(x+17)=0

Solution for (x+3)(x+17)=0 equation:

Simplifying
(x + 3)(x + 17) = 0

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

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

Multiply (3 + x) * (17 + x)
(3(17 + x) + x(17 + x)) = 0
((17 * 3 + x * 3) + x(17 + x)) = 0
((51 + 3x) + x(17 + x)) = 0
(51 + 3x + (17 * x + x * x)) = 0
(51 + 3x + (17x + x2)) = 0

Combine like terms: 3x + 17x = 20x
(51 + 20x + x2) = 0

Solving
51 + 20x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(17 + x)(3 + 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 '(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 = {-17, -3}