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

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

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

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

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

Combine like terms: 18z + -8z = 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}