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

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

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

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

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

Combine like terms: 9z + -1z = 8z
(-3 + 8z + 3z2) = 0

Solving
-3 + 8z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(1 + -3z) = 0

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

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

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

Divide each side by '-1'.
z = -3

Simplifying
z = -3
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 = {-3, 0.3333333333}