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

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

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

Combine like terms: 5z + z = 6z
(6z)(2 + z) = 0

Remove parenthesis around (6z)
6z(2 + z) = 0
(2 * 6z + z * 6z) = 0
(12z + 6z2) = 0

Solving
12z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '6z'.
6z(2 + z) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
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 = {0, -2}