(2z+9)(4+z)=0

Solution for (2z+9)(4+z)=0 equation:

Simplifying
(2z + 9)(4 + z) = 0

Reorder the terms:
(9 + 2z)(4 + z) = 0

Multiply (9 + 2z) * (4 + z)
(9(4 + z) + 2z * (4 + z)) = 0
((4 * 9 + z * 9) + 2z * (4 + z)) = 0
((36 + 9z) + 2z * (4 + z)) = 0
(36 + 9z + (4 * 2z + z * 2z)) = 0
(36 + 9z + (8z + 2z2)) = 0

Combine like terms: 9z + 8z = 17z
(36 + 17z + 2z2) = 0

Solving
36 + 17z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + 2z)(4 + z) = 0

Subproblem 1
Set the factor '(9 + 2z)' equal to zero and attempt to solve:

Simplifying
9 + 2z = 0

Solving
9 + 2z = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2z = 0 + -9
2z = 0 + -9

Combine like terms: 0 + -9 = -9
2z = -9

Divide each side by '2'.
z = -4.5

Simplifying
z = -4.5
Subproblem 2
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

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

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

Simplifying
z = -4
Solution
z = {-4.5, -4}