24a^2+186a-540=0

Solution for 24a^2+186a-540=0 equation:

Simplifying
24a2 + 186a + -540 = 0

Reorder the terms:
-540 + 186a + 24a2 = 0

Solving
-540 + 186a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-90 + 31a + 4a2) = 0

Factor a trinomial.
6((-10 + -1a)(9 + -4a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-10 + -1a)' equal to zero and attempt to solve:

Simplifying
-10 + -1a = 0

Solving
-10 + -1a = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1a = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1a = 0 + 10
-1a = 0 + 10

Combine like terms: 0 + 10 = 10
-1a = 10

Divide each side by '-1'.
a = -10

Simplifying
a = -10
Subproblem 2
Set the factor '(9 + -4a)' equal to zero and attempt to solve:

Simplifying
9 + -4a = 0

Solving
9 + -4a = 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 + -4a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4a = 0 + -9
-4a = 0 + -9

Combine like terms: 0 + -9 = -9
-4a = -9

Divide each side by '-4'.
a = 2.25

Simplifying
a = 2.25
Solution
a = {-10, 2.25}