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

Solution for (3z+1)(5-z)=0 equation:

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

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

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

Combine like terms: -1z + 15z = 14z
(5 + 14z + -3z2) = 0

Solving
5 + 14z + -3z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Subproblem 2
Set the factor '(1 + 3z)' equal to zero and attempt to solve:

Simplifying
1 + 3z = 0

Solving
1 + 3z = 0

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

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

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

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

Divide each side by '3'.
z = -0.3333333333

Simplifying
z = -0.3333333333
Solution
z = {5, -0.3333333333}