24v^4+78v^3b-21v^2b^2=0

Solution for 24v^4+78v^3b-21v^2b^2=0 equation:

Simplifying
24v4 + 78v3b + -21v2b2 = 0

Reorder the terms:
78bv3 + -21b2v2 + 24v4 = 0

Solving
78bv3 + -21b2v2 + 24v4 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3v2'.
3v2(26bv + -7b2 + 8v2) = 0

Factor a trinomial.
3v2((-7b + -2v)(b + -4v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Add '-1v2' to each side of the equation.
v2 + -1v2 = 0 + -1v2
Remove the zero:
0 = -1v2

Simplifying
0 = -1v2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-7b + -2v)' equal to zero and attempt to solve:

Simplifying
-7b + -2v = 0

Solving
-7b + -2v = 0

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

Add '2v' to each side of the equation.
-7b + -2v + 2v = 0 + 2v

Combine like terms: -2v + 2v = 0
-7b + 0 = 0 + 2v
-7b = 0 + 2v
Remove the zero:
-7b = 2v

Divide each side by '-7'.
b = -0.2857142857v

Simplifying
b = -0.2857142857v
Subproblem 3
Set the factor '(b + -4v)' equal to zero and attempt to solve:

Simplifying
b + -4v = 0

Solving
b + -4v = 0

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

Add '4v' to each side of the equation.
b + -4v + 4v = 0 + 4v

Combine like terms: -4v + 4v = 0
b + 0 = 0 + 4v
b = 0 + 4v
Remove the zero:
b = 4v

Simplifying
b = 4v
Solution
b = {-0.2857142857v, 4v}