9z^2+19z-138=0

Solution for 9z^2+19z-138=0 equation:

Simplifying
9z2 + 19z + -138 = 0

Reorder the terms:
-138 + 19z + 9z2 = 0

Solving
-138 + 19z + 9z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-46 + -9z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-46 + -9z)' equal to zero and attempt to solve:

Simplifying
-46 + -9z = 0

Solving
-46 + -9z = 0

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

Add '46' to each side of the equation.
-46 + 46 + -9z = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -9z = 0 + 46
-9z = 0 + 46

Combine like terms: 0 + 46 = 46
-9z = 46

Divide each side by '-9'.
z = -5.111111111

Simplifying
z = -5.111111111
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-5.111111111, 3}