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

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

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

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

Multiply (6 + 5z) * (3 + -1z)
(6(3 + -1z) + 5z * (3 + -1z)) = 0
((3 * 6 + -1z * 6) + 5z * (3 + -1z)) = 0
((18 + -6z) + 5z * (3 + -1z)) = 0
(18 + -6z + (3 * 5z + -1z * 5z)) = 0
(18 + -6z + (15z + -5z2)) = 0

Combine like terms: -6z + 15z = 9z
(18 + 9z + -5z2) = 0

Solving
18 + 9z + -5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(6 + 5z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(6 + 5z)' equal to zero and attempt to solve:

Simplifying
6 + 5z = 0

Solving
6 + 5z = 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 + 5z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5z = 0 + -6
5z = 0 + -6

Combine like terms: 0 + -6 = -6
5z = -6

Divide each side by '5'.
z = -1.2

Simplifying
z = -1.2
Solution
z = {3, -1.2}