6a^2-7a-24=0

Solution for 6a^2-7a-24=0 equation:

Simplifying
6a2 + -7a + -24 = 0

Reorder the terms:
-24 + -7a + 6a2 = 0

Solving
-24 + -7a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -2a)(8 + -3a) = 0

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

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(8 + -3a)' equal to zero and attempt to solve:

Simplifying
8 + -3a = 0

Solving
8 + -3a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a = 0 + -8
-3a = 0 + -8

Combine like terms: 0 + -8 = -8
-3a = -8

Divide each side by '-3'.
a = 2.666666667

Simplifying
a = 2.666666667
Solution
a = {-1.5, 2.666666667}