(1-z)(2z+5)=0

Solution for (1-z)(2z+5)=0 equation:

Simplifying
(1 + -1z)(2z + 5) = 0

Reorder the terms:
(1 + -1z)(5 + 2z) = 0

Multiply (1 + -1z) * (5 + 2z)
(1(5 + 2z) + -1z * (5 + 2z)) = 0
((5 * 1 + 2z * 1) + -1z * (5 + 2z)) = 0
((5 + 2z) + -1z * (5 + 2z)) = 0
(5 + 2z + (5 * -1z + 2z * -1z)) = 0
(5 + 2z + (-5z + -2z2)) = 0

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

Solving
5 + -3z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -1z)(5 + 2z) = 0

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

Simplifying
1 + -1z = 0

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

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

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

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

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

Simplifying
5 + 2z = 0

Solving
5 + 2z = 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 + 2z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2z = 0 + -5
2z = 0 + -5

Combine like terms: 0 + -5 = -5
2z = -5

Divide each side by '2'.
z = -2.5

Simplifying
z = -2.5
Solution
z = {1, -2.5}