3a^2(a-5)=72a

Solution for 3a^2(a-5)=72a equation:

Simplifying
3a2(a + -5) = 72a

Reorder the terms:
3a2(-5 + a) = 72a
(-5 * 3a2 + a * 3a2) = 72a
(-15a2 + 3a3) = 72a

Solving
-15a2 + 3a3 = 72a

Solving for variable 'a'.

Reorder the terms:
-72a + -15a2 + 3a3 = 72a + -72a

Combine like terms: 72a + -72a = 0
-72a + -15a2 + 3a3 = 0

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-24 + -5a + a2) = 0

Factor a trinomial.
3a((-3 + -1a)(8 + -1a)) = 0

Ignore the factor 3.
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 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 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 + -1a = 0 + 3

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

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

Divide each side by '-1'.
a = -3

Simplifying
a = -3
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, -3, 8}