(2z+1)(5+z)=0

Solution for (2z+1)(5+z)=0 equation:

Simplifying
(2z + 1)(5 + z) = 0

Reorder the terms:
(1 + 2z)(5 + z) = 0

Multiply (1 + 2z) * (5 + z)
(1(5 + z) + 2z * (5 + z)) = 0
((5 * 1 + z * 1) + 2z * (5 + z)) = 0
((5 + 1z) + 2z * (5 + z)) = 0
(5 + 1z + (5 * 2z + z * 2z)) = 0
(5 + 1z + (10z + 2z2)) = 0

Combine like terms: 1z + 10z = 11z
(5 + 11z + 2z2) = 0

Solving
5 + 11z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(5 + z)(1 + 2z) = 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 '(1 + 2z)' equal to zero and attempt to solve:

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-5, -0.5}