24p^2-5p-1=0

Solution for 24p^2-5p-1=0 equation:

Simplifying
24p2 + -5p + -1 = 0

Reorder the terms:
-1 + -5p + 24p2 = 0

Solving
-1 + -5p + 24p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -8p)(1 + -3p) = 0

Subproblem 1
Set the factor '(-1 + -8p)' equal to zero and attempt to solve:

Simplifying
-1 + -8p = 0

Solving
-1 + -8p = 0

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

Add '1' to each side of the equation.
-1 + 1 + -8p = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8p = 0 + 1
-8p = 0 + 1

Combine like terms: 0 + 1 = 1
-8p = 1

Divide each side by '-8'.
p = -0.125

Simplifying
p = -0.125
Subproblem 2
Set the factor '(1 + -3p)' equal to zero and attempt to solve:

Simplifying
1 + -3p = 0

Solving
1 + -3p = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3p = 0 + -1

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

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

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

Simplifying
p = 0.3333333333
Solution
p = {-0.125, 0.3333333333}