3z^2-19z+30=0

Solution for 3z^2-19z+30=0 equation:

Simplifying
3z2 + -19z + 30 = 0

Reorder the terms:
30 + -19z + 3z2 = 0

Solving
30 + -19z + 3z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -3z)' equal to zero and attempt to solve:

Simplifying
10 + -3z = 0

Solving
10 + -3z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3z = 0 + -10
-3z = 0 + -10

Combine like terms: 0 + -10 = -10
-3z = -10

Divide each side by '-3'.
z = 3.333333333

Simplifying
z = 3.333333333
Solution
z = {3, 3.333333333}