24a^2+36a-24=0

Solution for 24a^2+36a-24=0 equation:

Simplifying
24a2 + 36a + -24 = 0

Reorder the terms:
-24 + 36a + 24a2 = 0

Solving
-24 + 36a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-2 + 3a + 2a2) = 0

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

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

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 2
Set the factor '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {-2, 0.5}