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

Solution for (2-z)(3z+1)=0 equation:

Simplifying
(2 + -1z)(3z + 1) = 0

Reorder the terms:
(2 + -1z)(1 + 3z) = 0

Multiply (2 + -1z) * (1 + 3z)
(2(1 + 3z) + -1z * (1 + 3z)) = 0
((1 * 2 + 3z * 2) + -1z * (1 + 3z)) = 0
((2 + 6z) + -1z * (1 + 3z)) = 0
(2 + 6z + (1 * -1z + 3z * -1z)) = 0
(2 + 6z + (-1z + -3z2)) = 0

Combine like terms: 6z + -1z = 5z
(2 + 5z + -3z2) = 0

Solving
2 + 5z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -1z)(1 + 3z) = 0

Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
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 = {2, -0.3333333333}