(-2z^3+z+2z^3+z)+(3z^3-5z^2)=

Solution for (-2z^3+z+2z^3+z)+(3z^3-5z^2)= equation:

Simplifying
(-2z3 + z + 2z3 + z) + (3z3 + -5z2) = 0

Reorder the terms:
(z + z + -2z3 + 2z3) + (3z3 + -5z2) = 0

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

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

Reorder the terms:
(2z) + (-5z2 + 3z3) = 0

Remove parenthesis around (-5z2 + 3z3)
(2z) + -5z2 + 3z3 = 0

Solving
(2z) + -5z2 + 3z3 = 0

Solving for variable 'z'.

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

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

Simplifying
2 + -3z = 0

Solving
2 + -3z = 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 + -3z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3z = 0 + -2
-3z = 0 + -2

Combine like terms: 0 + -2 = -2
-3z = -2

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Subproblem 3
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

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

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

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

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

Simplifying
z = 1
Solution
z = {0, 0.6666666667, 1}