(x+5)(x+12)=0

Solution for (x+5)(x+12)=0 equation:

Simplifying
(x + 5)(x + 12) = 0

Reorder the terms:
(5 + x)(x + 12) = 0

Reorder the terms:
(5 + x)(12 + x) = 0

Multiply (5 + x) * (12 + x)
(5(12 + x) + x(12 + x)) = 0
((12 * 5 + x * 5) + x(12 + x)) = 0
((60 + 5x) + x(12 + x)) = 0
(60 + 5x + (12 * x + x * x)) = 0
(60 + 5x + (12x + x2)) = 0

Combine like terms: 5x + 12x = 17x
(60 + 17x + x2) = 0

Solving
60 + 17x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(12 + x)(5 + x) = 0

Subproblem 1
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-12, -5}