(x+5)(x+10)=0

Solution for (x+5)(x+10)=0 equation:

Simplifying
(x + 5)(x + 10) = 0

Reorder the terms:
(5 + x)(x + 10) = 0

Reorder the terms:
(5 + x)(10 + x) = 0

Multiply (5 + x) * (10 + x)
(5(10 + x) + x(10 + x)) = 0
((10 * 5 + x * 5) + x(10 + x)) = 0
((50 + 5x) + x(10 + x)) = 0
(50 + 5x + (10 * x + x * x)) = 0
(50 + 5x + (10x + x2)) = 0

Combine like terms: 5x + 10x = 15x
(50 + 15x + x2) = 0

Solving
50 + 15x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
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 = {-10, -5}