4z^3+16z^2=48z

Solution for 4z^3+16z^2=48z equation:

Simplifying
4z3 + 16z2 = 48z

Reorder the terms:
16z2 + 4z3 = 48z

Solving
16z2 + 4z3 = 48z

Solving for variable 'z'.

Reorder the terms:
-48z + 16z2 + 4z3 = 48z + -48z

Combine like terms: 48z + -48z = 0
-48z + 16z2 + 4z3 = 0

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-12 + 4z + z2) = 0

Factor a trinomial.
4z((-6 + -1z)(2 + -1z)) = 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 '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 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 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 3
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {0, -6, 2}