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

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

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

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

Multiply (-8 + 3z) * (6 + z)
(-8(6 + z) + 3z * (6 + z)) = 0
((6 * -8 + z * -8) + 3z * (6 + z)) = 0
((-48 + -8z) + 3z * (6 + z)) = 0
(-48 + -8z + (6 * 3z + z * 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}