(x+3)*(x+5)=0

Solution for (x+3)*(x+5)=0 equation:

Simplifying
(x + 3)(x + 5) = 0

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

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

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) = 0
((5 * 3 + x * 3) + x(5 + x)) = 0
((15 + 3x) + x(5 + x)) = 0
(15 + 3x + (5 * x + x * x)) = 0
(15 + 3x + (5x + x2)) = 0

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) = 0

Solving
15 + 8x + x2 = 0

Solving for variable 'x'.

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

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}