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

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

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

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

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

Combine like terms: 15z + -6z = 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}