(3z+8)(6-z)=0

Solution for (3z+8)(6-z)=0 equation:

Simplifying
(3z + 8)(6 + -1z) = 0

Reorder the terms:
(8 + 3z)(6 + -1z) = 0

Multiply (8 + 3z) * (6 + -1z)
(8(6 + -1z) + 3z * (6 + -1z)) = 0
((6 * 8 + -1z * 8) + 3z * (6 + -1z)) = 0
((48 + -8z) + 3z * (6 + -1z)) = 0
(48 + -8z + (6 * 3z + -1z * 3z)) = 0
(48 + -8z + (18z + -3z2)) = 0

Combine like terms: -8z + 18z = 10z
(48 + 10z + -3z2) = 0

Solving
48 + 10z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(8 + 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 '(8 + 3z)' equal to zero and attempt to solve:

Simplifying
8 + 3z = 0

Solving
8 + 3z = 0

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

Add '-8' to each side of the equation.
8 + -8 + 3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3z = 0 + -8
3z = 0 + -8

Combine like terms: 0 + -8 = -8
3z = -8

Divide each side by '3'.
z = -2.666666667

Simplifying
z = -2.666666667
Solution
z = {6, -2.666666667}