(2+z)(4z+5)=0

Solution for (2+z)(4z+5)=0 equation:

Simplifying
(2 + z)(4z + 5) = 0

Reorder the terms:
(2 + z)(5 + 4z) = 0

Multiply (2 + z) * (5 + 4z)
(2(5 + 4z) + z(5 + 4z)) = 0
((5 * 2 + 4z * 2) + z(5 + 4z)) = 0
((10 + 8z) + z(5 + 4z)) = 0
(10 + 8z + (5 * z + 4z * z)) = 0
(10 + 8z + (5z + 4z2)) = 0

Combine like terms: 8z + 5z = 13z
(10 + 13z + 4z2) = 0

Solving
10 + 13z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + z)(5 + 4z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve:

Simplifying
5 + 4z = 0

Solving
5 + 4z = 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 + 4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4z = 0 + -5
4z = 0 + -5

Combine like terms: 0 + -5 = -5
4z = -5

Divide each side by '4'.
z = -1.25

Simplifying
z = -1.25
Solution
z = {-2, -1.25}