2z^2-19z+30=0

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

Simplifying
2z2 + -19z + 30 = 0

Reorder the terms:
30 + -19z + 2z2 = 0

Solving
30 + -19z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -1z)(15 + -2z) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Subproblem 2
Set the factor '(15 + -2z)' equal to zero and attempt to solve:

Simplifying
15 + -2z = 0

Solving
15 + -2z = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2z = 0 + -15
-2z = 0 + -15

Combine like terms: 0 + -15 = -15
-2z = -15

Divide each side by '-2'.
z = 7.5

Simplifying
z = 7.5
Solution
z = {2, 7.5}