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

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

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

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

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