4ax^2+4ax-24a=0

Solution for 4ax^2+4ax-24a=0 equation:

Simplifying
4ax2 + 4ax + -24a = 0

Reorder the terms:
-24a + 4ax + 4ax2 = 0

Solving
-24a + 4ax + 4ax2 = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-6 + x + x2) = 0

Factor a trinomial.
4a((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Add 'x' to each side of the equation.
-1x + x = 3 + x

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

Simplifying
0 = 3 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Add 'x' to each side of the equation.
-1x + x = -2 + x

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

Simplifying
0 = -2 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}