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

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

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

Reorder the terms:
x(2 + x) + 5(x + 2) = 0
(2 * x + x * x) + 5(x + 2) = 0
(2x + x2) + 5(x + 2) = 0

Reorder the terms:
2x + x2 + 5(2 + x) = 0
2x + x2 + (2 * 5 + x * 5) = 0
2x + x2 + (10 + 5x) = 0

Reorder the terms:
10 + 2x + 5x + x2 = 0

Combine like terms: 2x + 5x = 7x
10 + 7x + x2 = 0

Solving
10 + 7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-5, -2}