24a^4+10a^3b-4a^2b^2=

Solution for 24a^4+10a^3b-4a^2b^2= equation:

Simplifying
24a4 + 10a3b + -4a2b2 = 0

Reorder the terms:
-4a2b2 + 10a3b + 24a4 = 0

Solving
-4a2b2 + 10a3b + 24a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(-2b2 + 5ab + 12a2) = 0

Factor a trinomial.
2a2((-2b + -3a)(b + -4a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(-2b + -3a)' equal to zero and attempt to solve:

Simplifying
-2b + -3a = 0

Reorder the terms:
-3a + -2b = 0

Solving
-3a + -2b = 0

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

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

Combine like terms: -2b + 2b = 0
-3a + 0 = 0 + 2b
-3a = 0 + 2b
Remove the zero:
-3a = 2b

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

Simplifying
a = -0.6666666667b
Subproblem 3
Set the factor '(b + -4a)' equal to zero and attempt to solve:

Simplifying
b + -4a = 0

Reorder the terms:
-4a + b = 0

Solving
-4a + b = 0

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

Add '-1b' to each side of the equation.
-4a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-4a + 0 = 0 + -1b
-4a = 0 + -1b
Remove the zero:
-4a = -1b

Divide each side by '-4'.
a = 0.25b

Simplifying
a = 0.25b
Solution
a = {0, -0.6666666667b, 0.25b}