20z^2-27z-8=

Solution for 20z^2-27z-8= equation:

Simplifying
20z2 + -27z + -8 = 0

Reorder the terms:
-8 + -27z + 20z2 = 0

Solving
-8 + -27z + 20z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -4z)(8 + -5z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -5z)' equal to zero and attempt to solve:

Simplifying
8 + -5z = 0

Solving
8 + -5z = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5z = 0 + -8
-5z = 0 + -8

Combine like terms: 0 + -8 = -8
-5z = -8

Divide each side by '-5'.
z = 1.6

Simplifying
z = 1.6
Solution
z = {-0.25, 1.6}