(a^2-4a)(-24-6a)=

Solution for (a^2-4a)(-24-6a)= equation:

Simplifying
(a2 + -4a)(-24 + -6a) = 0

Reorder the terms:
(-4a + a2)(-24 + -6a) = 0

Multiply (-4a + a2) * (-24 + -6a)
(-4a * (-24 + -6a) + a2(-24 + -6a)) = 0
((-24 * -4a + -6a * -4a) + a2(-24 + -6a)) = 0
((96a + 24a2) + a2(-24 + -6a)) = 0
(96a + 24a2 + (-24 * a2 + -6a * a2)) = 0
(96a + 24a2 + (-24a2 + -6a3)) = 0

Combine like terms: 24a2 + -24a2 = 0
(96a + 0 + -6a3) = 0
(96a + -6a3) = 0

Solving
96a + -6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6a'.
6a(16 + -1a2) = 0

Factor a difference between two squares.
6a((4 + a)(4 + -1a)) = 0

Ignore the factor 6.
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 '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

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

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Subproblem 3
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

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

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {0, -4, 4}