8p^2+19p-105=0

Solution for 8p^2+19p-105=0 equation:

Simplifying
8p2 + 19p + -105 = 0

Reorder the terms:
-105 + 19p + 8p2 = 0

Solving
-105 + 19p + 8p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5 + -1p)(21 + -8p) = 0

Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5
Subproblem 2
Set the factor '(21 + -8p)' equal to zero and attempt to solve:

Simplifying
21 + -8p = 0

Solving
21 + -8p = 0

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

Add '-21' to each side of the equation.
21 + -21 + -8p = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -8p = 0 + -21
-8p = 0 + -21

Combine like terms: 0 + -21 = -21
-8p = -21

Divide each side by '-8'.
p = 2.625

Simplifying
p = 2.625
Solution
p = {-5, 2.625}