z^2+z+4z^3+4z^2=

Solution for z^2+z+4z^3+4z^2= equation:

Simplifying
z2 + z + 4z3 + 4z2 = 0

Reorder the terms:
z + z2 + 4z2 + 4z3 = 0

Combine like terms: z2 + 4z2 = 5z2
z + 5z2 + 4z3 = 0

Solving
z + 5z2 + 4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(1 + 5z + 4z2) = 0

Factor a trinomial.
z((1 + z)(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 '(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 + 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, -1, -0.25}