48z^3+24z^2-45z=

Solution for 48z^3+24z^2-45z= equation:

Simplifying
48z3 + 24z2 + -45z = 0

Reorder the terms:
-45z + 24z2 + 48z3 = 0

Solving
-45z + 24z2 + 48z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-15 + 8z + 16z2) = 0

Factor a trinomial.
3z((-5 + -4z)(3 + -4z)) = 0

Ignore the factor 3.
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 '(-5 + -4z)' equal to zero and attempt to solve:

Simplifying
-5 + -4z = 0

Solving
-5 + -4z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4z = 0 + 5
-4z = 0 + 5

Combine like terms: 0 + 5 = 5
-4z = 5

Divide each side by '-4'.
z = -1.25

Simplifying
z = -1.25
Subproblem 3
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {0, -1.25, 0.75}