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.
(15 + 2z)(2 + z) = 0

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

Simplifying
2 + z = 0

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

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

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

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