z(z+5)+2(z+5)=0

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

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

Reorder the terms:
z(5 + z) + 2(z + 5) = 0
(5 * z + z * z) + 2(z + 5) = 0
(5z + z2) + 2(z + 5) = 0

Reorder the terms:
5z + z2 + 2(5 + z) = 0
5z + z2 + (5 * 2 + z * 2) = 0
5z + z2 + (10 + 2z) = 0

Reorder the terms:
10 + 5z + 2z + z2 = 0

Combine like terms: 5z + 2z = 7z
10 + 7z + z2 = 0

Solving
10 + 7z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + z)(2 + z) = 0

Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

Solving
5 + z = 0

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

Add '-5' to each side of the equation.
5 + -5 + z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + z = 0 + -5
z = 0 + -5

Combine like terms: 0 + -5 = -5
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 0

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

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

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

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

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