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

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

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

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

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

Multiply (-1 + 2z) * (5 + z)
(-1(5 + z) + 2z * (5 + z)) = 0
((5 * -1 + z * -1) + 2z * (5 + z)) = 0
((-5 + -1z) + 2z * (5 + z)) = 0
(-5 + -1z + (5 * 2z + z * 2z)) = 0
(-5 + -1z + (10z + 2z2)) = 0

Combine like terms: -1z + 10z = 9z
(-5 + 9z + 2z2) = 0

Solving
-5 + 9z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z)(1 + -2z) = 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 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

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

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

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-5, 0.5}