8z^3+38z^2+9z=

Solution for 8z^3+38z^2+9z= equation:

Simplifying
8z3 + 38z2 + 9z = 0

Reorder the terms:
9z + 38z2 + 8z3 = 0

Solving
9z + 38z2 + 8z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(9 + 38z + 8z2) = 0

Factor a trinomial.
z((9 + 2z)(1 + 4z)) = 0

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(9 + 2z)' equal to zero and attempt to solve:

Simplifying
9 + 2z = 0

Solving
9 + 2z = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2z = 0 + -9
2z = 0 + -9

Combine like terms: 0 + -9 = -9
2z = -9

Divide each side by '2'.
z = -4.5

Simplifying
z = -4.5
Subproblem 3
Set the factor '(1 + 4z)' equal to zero and attempt to solve:

Simplifying
1 + 4z = 0

Solving
1 + 4z = 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 + 4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z = 0 + -1
4z = 0 + -1

Combine like terms: 0 + -1 = -1
4z = -1

Divide each side by '4'.
z = -0.25

Simplifying
z = -0.25
Solution
z = {0, -4.5, -0.25}