4b^4-24b^3=-36b^2

Solution for 4b^4-24b^3=-36b^2 equation:

Simplifying
4b4 + -24b3 = -36b2

Reorder the terms:
-24b3 + 4b4 = -36b2

Solving
-24b3 + 4b4 = -36b2

Solving for variable 'b'.

Reorder the terms:
36b2 + -24b3 + 4b4 = -36b2 + 36b2

Combine like terms: -36b2 + 36b2 = 0
36b2 + -24b3 + 4b4 = 0

Factor out the Greatest Common Factor (GCF), '4b2'.
4b2(9 + -6b + b2) = 0

Factor a trinomial.
4b2((3 + -1b)(3 + -1b)) = 0

Ignore the factor 4.
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 '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

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

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

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

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

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

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

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

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

Simplifying
b = 3
Solution
b = {0, 3, 3}