(2z-1)(z+4)=0

Solution for (2z-1)(z+4)=0 equation:

Simplifying
(2z + -1)(z + 4) = 0

Reorder the terms:
(-1 + 2z)(z + 4) = 0

Reorder the terms:
(-1 + 2z)(4 + z) = 0

Multiply (-1 + 2z) * (4 + z)
(-1(4 + z) + 2z * (4 + z)) = 0
((4 * -1 + z * -1) + 2z * (4 + z)) = 0
((-4 + -1z) + 2z * (4 + z)) = 0
(-4 + -1z + (4 * 2z + z * 2z)) = 0
(-4 + -1z + (8z + 2z2)) = 0

Combine like terms: -1z + 8z = 7z
(-4 + 7z + 2z2) = 0

Solving
-4 + 7z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(1 + -2z) = 0

Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
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 = {-4, 0.5}