(3z+1)(6-z)=0

Solution for (3z+1)(6-z)=0 equation:

Simplifying
(3z + 1)(6 + -1z) = 0

Reorder the terms:
(1 + 3z)(6 + -1z) = 0

Multiply (1 + 3z) * (6 + -1z)
(1(6 + -1z) + 3z * (6 + -1z)) = 0
((6 * 1 + -1z * 1) + 3z * (6 + -1z)) = 0
((6 + -1z) + 3z * (6 + -1z)) = 0
(6 + -1z + (6 * 3z + -1z * 3z)) = 0
(6 + -1z + (18z + -3z2)) = 0

Combine like terms: -1z + 18z = 17z
(6 + 17z + -3z2) = 0

Solving
6 + 17z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(1 + 3z) = 0

Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
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 = {6, -0.3333333333}