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

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

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

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

Multiply (9 + Z) * (1 + 4Z)
(9(1 + 4Z) + Z(1 + 4Z)) = 0
((1 * 9 + 4Z * 9) + Z(1 + 4Z)) = 0
((9 + 36Z) + Z(1 + 4Z)) = 0
(9 + 36Z + (1 * Z + 4Z * Z)) = 0
(9 + 36Z + (1Z + 4Z2)) = 0

Combine like terms: 36Z + 1Z = 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}