3a^2-6a=72

Solution for 3a^2-6a=72 equation:

Simplifying
3a2 + -6a = 72

Reorder the terms:
-6a + 3a2 = 72

Solving
-6a + 3a2 = 72

Solving for variable 'a'.

Reorder the terms:
-72 + -6a + 3a2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -6a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + -2a + a2) = 0

Factor a trinomial.
3((-4 + -1a)(6 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-4, 6}