5z^2-12z-32=0

Solution for 5z^2-12z-32=0 equation:

Simplifying
5z2 + -12z + -32 = 0

Reorder the terms:
-32 + -12z + 5z2 = 0

Solving
-32 + -12z + 5z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
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
Solution
z = {-1.6, 4}