(4z+1)(9+z)=0

Solution for (4z+1)(9+z)=0 equation:

Simplifying
(4z + 1)(9 + z) = 0

Reorder the terms:
(1 + 4z)(9 + z) = 0

Multiply (1 + 4z) * (9 + z)
(1(9 + z) + 4z * (9 + z)) = 0
((9 * 1 + z * 1) + 4z * (9 + z)) = 0
((9 + 1z) + 4z * (9 + z)) = 0
(9 + 1z + (9 * 4z + z * 4z)) = 0
(9 + 1z + (36z + 4z2)) = 0

Combine like terms: 1z + 36z = 37z
(9 + 37z + 4z2) = 0

Solving
9 + 37z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + z)(1 + 4z) = 0

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

Simplifying
9 + z = 0

Solving
9 + z = 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 + z = 0 + -9

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

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

Simplifying
z = -9
Subproblem 2
Set the factor '(1 + 4z)' equal to zero and attempt to solve:

Simplifying
1 + 4z = 0

Solving
1 + 4z = 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 + 4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z = 0 + -1
4z = 0 + -1

Combine like terms: 0 + -1 = -1
4z = -1

Divide each side by '4'.
z = -0.25

Simplifying
z = -0.25
Solution
z = {-9, -0.25}