60b^4+102b^3+36b^2=0

Solution for 60b^4+102b^3+36b^2=0 equation:

Simplifying
60b4 + 102b3 + 36b2 = 0

Reorder the terms:
36b2 + 102b3 + 60b4 = 0

Solving
36b2 + 102b3 + 60b4 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '6b2'.
6b2(6 + 17b + 10b2) = 0

Factor a trinomial.
6b2((6 + 5b)(1 + 2b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve:

Simplifying
b2 = 0

Solving
b2 = 0

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

Simplifying
b2 = 0

Take the square root of each side:
b = {0}
Subproblem 2
Set the factor '(6 + 5b)' equal to zero and attempt to solve:

Simplifying
6 + 5b = 0

Solving
6 + 5b = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5b = 0 + -6
5b = 0 + -6

Combine like terms: 0 + -6 = -6
5b = -6

Divide each side by '5'.
b = -1.2

Simplifying
b = -1.2
Subproblem 3
Set the factor '(1 + 2b)' equal to zero and attempt to solve:

Simplifying
1 + 2b = 0

Solving
1 + 2b = 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 + 2b = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2b = 0 + -1
2b = 0 + -1

Combine like terms: 0 + -1 = -1
2b = -1

Divide each side by '2'.
b = -0.5

Simplifying
b = -0.5
Solution
b = {0, -1.2, -0.5}