=3b^3-5b^2+2b

Solution for =3b^3-5b^2+2b equation:

Simplifying
0 = 3b3 + -5b2 + 2b

Reorder the terms:
0 = 2b + -5b2 + 3b3

Solving
0 = 2b + -5b2 + 3b3

Solving for variable 'b'.
Remove the zero:
-2b + 5b2 + -3b3 = 2b + -5b2 + 3b3 + -2b + 5b2 + -3b3

Reorder the terms:
-2b + 5b2 + -3b3 = 2b + -2b + -5b2 + 5b2 + 3b3 + -3b3

Combine like terms: 2b + -2b = 0
-2b + 5b2 + -3b3 = 0 + -5b2 + 5b2 + 3b3 + -3b3
-2b + 5b2 + -3b3 = -5b2 + 5b2 + 3b3 + -3b3

Combine like terms: -5b2 + 5b2 = 0
-2b + 5b2 + -3b3 = 0 + 3b3 + -3b3
-2b + 5b2 + -3b3 = 3b3 + -3b3

Combine like terms: 3b3 + -3b3 = 0
-2b + 5b2 + -3b3 = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(-2 + 5b + -3b2) = 0

Factor a trinomial.
b((-1 + b)(2 + -3b)) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(-1 + b)' equal to zero and attempt to solve:

Simplifying
-1 + b = 0

Solving
-1 + b = 0

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

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

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

Combine like terms: 0 + 1 = 1
b = 1

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

Simplifying
2 + -3b = 0

Solving
2 + -3b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3b = 0 + -2

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

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

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

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