3a^2=-6a+72

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

Simplifying
3a2 = -6a + 72

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

Solving
3a2 = 72 + -6a

Solving for variable 'a'.

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

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

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

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

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

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

Ignore the factor 3.
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 '(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 = {-6, 4}