2a^2-12a=144

Solution for 2a^2-12a=144 equation:

Simplifying
2a2 + -12a = 144

Reorder the terms:
-12a + 2a2 = 144

Solving
-12a + 2a2 = 144

Solving for variable 'a'.

Reorder the terms:
-144 + -12a + 2a2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + -12a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -6a + a2) = 0

Factor a trinomial.
2((-6 + -1a)(12 + -1a)) = 0

Ignore the factor 2.
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 '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {-6, 12}