-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}