18z^2+19z-12=0

Solution for 18z^2+19z-12=0 equation:

Simplifying
18z2 + 19z + -12 = 0

Reorder the terms:
-12 + 19z + 18z2 = 0

Solving
-12 + 19z + 18z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -2z)(4 + -9z) = 0

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

Simplifying
-3 + -2z = 0

Solving
-3 + -2z = 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 + -2z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2z = 0 + 3
-2z = 0 + 3

Combine like terms: 0 + 3 = 3
-2z = 3

Divide each side by '-2'.
z = -1.5

Simplifying
z = -1.5
Subproblem 2
Set the factor '(4 + -9z)' equal to zero and attempt to solve:

Simplifying
4 + -9z = 0

Solving
4 + -9z = 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 + -9z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9z = 0 + -4
-9z = 0 + -4

Combine like terms: 0 + -4 = -4
-9z = -4

Divide each side by '-9'.
z = 0.4444444444

Simplifying
z = 0.4444444444
Solution
z = {-1.5, 0.4444444444}