24a^2-46a-18=0

Solution for 24a^2-46a-18=0 equation:

Simplifying
24a2 + -46a + -18 = 0

Reorder the terms:
-18 + -46a + 24a2 = 0

Solving
-18 + -46a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -23a + 12a2) = 0

Factor a trinomial.
2((-1 + -3a)(9 + -4a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3a)' equal to zero and attempt to solve:

Simplifying
-1 + -3a = 0

Solving
-1 + -3a = 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 + -3a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3a = 0 + 1
-3a = 0 + 1

Combine like terms: 0 + 1 = 1
-3a = 1

Divide each side by '-3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
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 = {-0.3333333333, 2.25}