(4z-2)(5+z)=0

Solution for (4z-2)(5+z)=0 equation:

Simplifying
(4z + -2)(5 + z) = 0

Reorder the terms:
(-2 + 4z)(5 + z) = 0

Multiply (-2 + 4z) * (5 + z)
(-2(5 + z) + 4z * (5 + z)) = 0
((5 * -2 + z * -2) + 4z * (5 + z)) = 0
((-10 + -2z) + 4z * (5 + z)) = 0
(-10 + -2z + (5 * 4z + z * 4z)) = 0
(-10 + -2z + (20z + 4z2)) = 0

Combine like terms: -2z + 20z = 18z
(-10 + 18z + 4z2) = 0

Solving
-10 + 18z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9z + 2z2) = 0

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

Ignore the factor 2.
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}