8z^3=-12z^2-4z

Solution for 8z^3=-12z^2-4z equation:

Simplifying
8z3 = -12z2 + -4z

Reorder the terms:
8z3 = -4z + -12z2

Solving
8z3 = -4z + -12z2

Solving for variable 'z'.

Reorder the terms:
4z + 12z2 + 8z3 = -4z + -12z2 + 4z + 12z2

Reorder the terms:
4z + 12z2 + 8z3 = -4z + 4z + -12z2 + 12z2

Combine like terms: -4z + 4z = 0
4z + 12z2 + 8z3 = 0 + -12z2 + 12z2
4z + 12z2 + 8z3 = -12z2 + 12z2

Combine like terms: -12z2 + 12z2 = 0
4z + 12z2 + 8z3 = 0

Factor out the Greatest Common Factor (GCF), '4z'.
4z(1 + 3z + 2z2) = 0

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

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

Simplifying
1 + z = 0

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

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

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

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

Simplifying
1 + 2z = 0

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

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

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

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {0, -1, -0.5}