12b^3+6b^2=18b

Solution for 12b^3+6b^2=18b equation:

Simplifying
12b3 + 6b2 = 18b

Reorder the terms:
6b2 + 12b3 = 18b

Solving
6b2 + 12b3 = 18b

Solving for variable 'b'.

Reorder the terms:
-18b + 6b2 + 12b3 = 18b + -18b

Combine like terms: 18b + -18b = 0
-18b + 6b2 + 12b3 = 0

Factor out the Greatest Common Factor (GCF), '6b'.
6b(-3 + b + 2b2) = 0

Factor a trinomial.
6b((-3 + -2b)(1 + -1b)) = 0

Ignore the factor 6.
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 '(-3 + -2b)' equal to zero and attempt to solve:

Simplifying
-3 + -2b = 0

Solving
-3 + -2b = 0

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

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

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

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

Divide each side by '-2'.
b = -1.5

Simplifying
b = -1.5
Subproblem 3
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 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 + -1b = 0 + -1

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

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

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

Simplifying
b = 1
Solution
b = {0, -1.5, 1}