2z^3-5z^2=3z

Solution for 2z^3-5z^2=3z equation:

Simplifying
2z3 + -5z2 = 3z

Reorder the terms:
-5z2 + 2z3 = 3z

Solving
-5z2 + 2z3 = 3z

Solving for variable 'z'.

Reorder the terms:
-3z + -5z2 + 2z3 = 3z + -3z

Combine like terms: 3z + -3z = 0
-3z + -5z2 + 2z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-3 + -5z + 2z2) = 0

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

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {0, -0.5, 3}