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

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

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

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

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

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

Combine like terms: 6x + 10x = 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}