(9+z)(3z+1)=0

Solution for (9+z)(3z+1)=0 equation:

Simplifying
(9 + z)(3z + 1) = 0

Reorder the terms:
(9 + z)(1 + 3z) = 0

Multiply (9 + z) * (1 + 3z)
(9(1 + 3z) + z(1 + 3z)) = 0
((1 * 9 + 3z * 9) + z(1 + 3z)) = 0
((9 + 27z) + z(1 + 3z)) = 0
(9 + 27z + (1 * z + 3z * z)) = 0
(9 + 27z + (1z + 3z2)) = 0

Combine like terms: 27z + 1z = 28z
(9 + 28z + 3z2) = 0

Solving
9 + 28z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(9 + z)(1 + 3z) = 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 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 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 + 3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3z = 0 + -1
3z = 0 + -1

Combine like terms: 0 + -1 = -1
3z = -1

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Solution
z = {-9, -0.3333333333}