-9z^2+9z-2=0

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

Simplifying
-9z2 + 9z + -2 = 0

Reorder the terms:
-2 + 9z + -9z2 = 0

Solving
-2 + 9z + -9z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + 3z)(1 + -3z) = 0

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

Simplifying
-2 + 3z = 0

Solving
-2 + 3z = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3z = 0 + 2

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

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

Divide each side by '3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

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

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

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

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {0.6666666667, 0.3333333333}