30z^2+96z+18=0

Solution for 30z^2+96z+18=0 equation:

Simplifying
30z2 + 96z + 18 = 0

Reorder the terms:
18 + 96z + 30z2 = 0

Solving
18 + 96z + 30z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 16z + 5z2) = 0

Factor a trinomial.
6((3 + z)(1 + 5z)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

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

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

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

Simplifying
z = -3
Subproblem 2
Set the factor '(1 + 5z)' equal to zero and attempt to solve:

Simplifying
1 + 5z = 0

Solving
1 + 5z = 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 + 5z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5z = 0 + -1
5z = 0 + -1

Combine like terms: 0 + -1 = -1
5z = -1

Divide each side by '5'.
z = -0.2

Simplifying
z = -0.2
Solution
z = {-3, -0.2}