5z^2-17z-12=0

Solution for 5z^2-17z-12=0 equation:

Simplifying
5z2 + -17z + -12 = 0

Reorder the terms:
-12 + -17z + 5z2 = 0

Solving
-12 + -17z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -5z)(4 + -1z) = 0

Subproblem 1
Set the factor '(-3 + -5z)' equal to zero and attempt to solve:

Simplifying
-3 + -5z = 0

Solving
-3 + -5z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5z = 0 + 3
-5z = 0 + 3

Combine like terms: 0 + 3 = 3
-5z = 3

Divide each side by '-5'.
z = -0.6

Simplifying
z = -0.6
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 = {-0.6, 4}