(6-z)(3z+5)=0

Solution for (6-z)(3z+5)=0 equation:

Simplifying
(6 + -1z)(3z + 5) = 0

Reorder the terms:
(6 + -1z)(5 + 3z) = 0

Multiply (6 + -1z) * (5 + 3z)
(6(5 + 3z) + -1z * (5 + 3z)) = 0
((5 * 6 + 3z * 6) + -1z * (5 + 3z)) = 0
((30 + 18z) + -1z * (5 + 3z)) = 0
(30 + 18z + (5 * -1z + 3z * -1z)) = 0
(30 + 18z + (-5z + -3z2)) = 0

Combine like terms: 18z + -5z = 13z
(30 + 13z + -3z2) = 0

Solving
30 + 13z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(5 + 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 '(5 + 3z)' equal to zero and attempt to solve:

Simplifying
5 + 3z = 0

Solving
5 + 3z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3z = 0 + -5
3z = 0 + -5

Combine like terms: 0 + -5 = -5
3z = -5

Divide each side by '3'.
z = -1.666666667

Simplifying
z = -1.666666667
Solution
z = {6, -1.666666667}