8z^2+30z+18=0

Solution for 8z^2+30z+18=0 equation:

Simplifying
8z2 + 30z + 18 = 0

Reorder the terms:
18 + 30z + 8z2 = 0

Solving
18 + 30z + 8z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 15z + 4z2) = 0

Factor a trinomial.
2((3 + z)(3 + 4z)) = 0

Ignore the factor 2.
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 '(3 + 4z)' equal to zero and attempt to solve:

Simplifying
3 + 4z = 0

Solving
3 + 4z = 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 + 4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4z = 0 + -3
4z = 0 + -3

Combine like terms: 0 + -3 = -3
4z = -3

Divide each side by '4'.
z = -0.75

Simplifying
z = -0.75
Solution
z = {-3, -0.75}