3z^4+42z^3+144z^2=

Solution for 3z^4+42z^3+144z^2= equation:

Simplifying
3z4 + 42z3 + 144z2 = 0

Reorder the terms:
144z2 + 42z3 + 3z4 = 0

Solving
144z2 + 42z3 + 3z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z2'.
3z2(48 + 14z + z2) = 0

Factor a trinomial.
3z2((8 + z)(6 + z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(8 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 0

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

Add '-8' to each side of the equation.
8 + -8 + z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + z = 0 + -8
z = 0 + -8

Combine like terms: 0 + -8 = -8
z = -8

Simplifying
z = -8
Subproblem 3
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

Add '-6' to each side of the equation.
6 + -6 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Solution
z = {0, -8, -6}