6a^2=72-24a

Solution for 6a^2=72-24a equation:

Simplifying
6a2 = 72 + -24a

Solving
6a2 = 72 + -24a

Solving for variable 'a'.

Reorder the terms:
-72 + 24a + 6a2 = 72 + -24a + -72 + 24a

Reorder the terms:
-72 + 24a + 6a2 = 72 + -72 + -24a + 24a

Combine like terms: 72 + -72 = 0
-72 + 24a + 6a2 = 0 + -24a + 24a
-72 + 24a + 6a2 = -24a + 24a

Combine like terms: -24a + 24a = 0
-72 + 24a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + 4a + a2) = 0

Factor a trinomial.
6((-6 + -1a)(2 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
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
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
Solution
a = {-6, 2}