4a^2(a-6)=64a

Solution for 4a^2(a-6)=64a equation:

Simplifying
4a2(a + -6) = 64a

Reorder the terms:
4a2(-6 + a) = 64a
(-6 * 4a2 + a * 4a2) = 64a
(-24a2 + 4a3) = 64a

Solving
-24a2 + 4a3 = 64a

Solving for variable 'a'.

Reorder the terms:
-64a + -24a2 + 4a3 = 64a + -64a

Combine like terms: 64a + -64a = 0
-64a + -24a2 + 4a3 = 0

Factor out the Greatest Common Factor (GCF), '4a'.
4a(-16 + -6a + a2) = 0

Factor a trinomial.
4a((-2 + -1a)(8 + -1a)) = 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 '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 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 + -1a = 0 + 2

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

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

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 3
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {0, -2, 8}