3a^2=-6a+144

Solution for 3a^2=-6a+144 equation:

Simplifying
3a2 = -6a + 144

Reorder the terms:
3a2 = 144 + -6a

Solving
3a2 = 144 + -6a

Solving for variable 'a'.

Reorder the terms:
-144 + 6a + 3a2 = 144 + -6a + -144 + 6a

Reorder the terms:
-144 + 6a + 3a2 = 144 + -144 + -6a + 6a

Combine like terms: 144 + -144 = 0
-144 + 6a + 3a2 = 0 + -6a + 6a
-144 + 6a + 3a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
-144 + 6a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-48 + 2a + a2) = 0

Factor a trinomial.
3((-8 + -1a)(6 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
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
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 = {-8, 6}