30z^2-23z+2=0

Solution for 30z^2-23z+2=0 equation:

Simplifying
30z2 + -23z + 2 = 0

Reorder the terms:
2 + -23z + 30z2 = 0

Solving
2 + -23z + 30z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + -10z)(2 + -3z) = 0

Subproblem 1
Set the factor '(1 + -10z)' equal to zero and attempt to solve:

Simplifying
1 + -10z = 0

Solving
1 + -10z = 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 + -10z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -10z = 0 + -1
-10z = 0 + -1

Combine like terms: 0 + -1 = -1
-10z = -1

Divide each side by '-10'.
z = 0.1

Simplifying
z = 0.1
Subproblem 2
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
Solution
z = {0.1, 0.6666666667}