3z^2+17z-20=0

Solution for 3z^2+17z-20=0 equation:

Simplifying
3z2 + 17z + -20 = 0

Reorder the terms:
-20 + 17z + 3z2 = 0

Solving
-20 + 17z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-20 + -3z)(1 + -1z) = 0

Subproblem 1
Set the factor '(-20 + -3z)' equal to zero and attempt to solve:

Simplifying
-20 + -3z = 0

Solving
-20 + -3z = 0

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

Add '20' to each side of the equation.
-20 + 20 + -3z = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3z = 0 + 20
-3z = 0 + 20

Combine like terms: 0 + 20 = 20
-3z = 20

Divide each side by '-3'.
z = -6.666666667

Simplifying
z = -6.666666667
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {-6.666666667, 1}