(x+5)(2x+6)=0

Solution for (x+5)(2x+6)=0 equation:

Simplifying
(x + 5)(2x + 6) = 0

Reorder the terms:
(5 + x)(2x + 6) = 0

Reorder the terms:
(5 + x)(6 + 2x) = 0

Multiply (5 + x) * (6 + 2x)
(5(6 + 2x) + x(6 + 2x)) = 0
((6 * 5 + 2x * 5) + x(6 + 2x)) = 0
((30 + 10x) + x(6 + 2x)) = 0
(30 + 10x + (6 * x + 2x * x)) = 0
(30 + 10x + (6x + 2x2)) = 0

Combine like terms: 10x + 6x = 16x
(30 + 16x + 2x2) = 0

Solving
30 + 16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 8x + x2) = 0

Factor a trinomial.
2((5 + x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-5, -3}