5p^2-39p-54=0

Solution for 5p^2-39p-54=0 equation:

Simplifying
5p2 + -39p + -54 = 0

Reorder the terms:
-54 + -39p + 5p2 = 0

Solving
-54 + -39p + 5p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-6 + -5p)(9 + -1p) = 0

Subproblem 1
Set the factor '(-6 + -5p)' equal to zero and attempt to solve:

Simplifying
-6 + -5p = 0

Solving
-6 + -5p = 0

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

Add '6' to each side of the equation.
-6 + 6 + -5p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5p = 0 + 6
-5p = 0 + 6

Combine like terms: 0 + 6 = 6
-5p = 6

Divide each side by '-5'.
p = -1.2

Simplifying
p = -1.2
Subproblem 2
Set the factor '(9 + -1p)' equal to zero and attempt to solve:

Simplifying
9 + -1p = 0

Solving
9 + -1p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1p = 0 + -9
-1p = 0 + -9

Combine like terms: 0 + -9 = -9
-1p = -9

Divide each side by '-1'.
p = 9

Simplifying
p = 9
Solution
p = {-1.2, 9}