0=24p^2-p-3

Solution for 0=24p^2-p-3 equation:

Simplifying
0 = 24p2 + -1p + -3

Reorder the terms:
0 = -3 + -1p + 24p2

Solving
0 = -3 + -1p + 24p2

Solving for variable 'p'.

Combine like terms: 0 + 3 = 3
3 + p + -24p2 = -3 + -1p + 24p2 + 3 + p + -24p2

Reorder the terms:
3 + p + -24p2 = -3 + 3 + -1p + p + 24p2 + -24p2

Combine like terms: -3 + 3 = 0
3 + p + -24p2 = 0 + -1p + p + 24p2 + -24p2
3 + p + -24p2 = -1p + p + 24p2 + -24p2

Combine like terms: -1p + p = 0
3 + p + -24p2 = 0 + 24p2 + -24p2
3 + p + -24p2 = 24p2 + -24p2

Combine like terms: 24p2 + -24p2 = 0
3 + p + -24p2 = 0

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

Subproblem 1
Set the factor '(3 + -8p)' equal to zero and attempt to solve:

Simplifying
3 + -8p = 0

Solving
3 + -8p = 0

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

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

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

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

Divide each side by '-8'.
p = 0.375

Simplifying
p = 0.375
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 = {0.375, -0.3333333333}