144=52a-4a^2

Solution for 144=52a-4a^2 equation:

Simplifying
144 = 52a + -4a2

Solving
144 = 52a + -4a2

Solving for variable 'a'.

Reorder the terms:
144 + -52a + 4a2 = 52a + -52a + -4a2 + 4a2

Combine like terms: 52a + -52a = 0
144 + -52a + 4a2 = 0 + -4a2 + 4a2
144 + -52a + 4a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
144 + -52a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + -13a + a2) = 0

Factor a trinomial.
4((4 + -1a)(9 + -1a)) = 0

Ignore the factor 4.
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 '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1a = 0 + -9
-1a = 0 + -9

Combine like terms: 0 + -9 = -9
-1a = -9

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Solution
a = {4, 9}