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

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

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

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

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

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

Solving
-2 + 7z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z)(1 + -4z) = 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 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

Solving
1 + -4z = 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 + -4z = 0 + -1

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

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

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Solution
z = {-2, 0.25}