3p^2-p-52=0

Solution for 3p^2-p-52=0 equation:

Simplifying
3p2 + -1p + -52 = 0

Reorder the terms:
-52 + -1p + 3p2 = 0

Solving
-52 + -1p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-4 + -1p)(13 + -3p) = 0

Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve:

Simplifying
-4 + -1p = 0

Solving
-4 + -1p = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1p = 0 + 4
-1p = 0 + 4

Combine like terms: 0 + 4 = 4
-1p = 4

Divide each side by '-1'.
p = -4

Simplifying
p = -4
Subproblem 2
Set the factor '(13 + -3p)' equal to zero and attempt to solve:

Simplifying
13 + -3p = 0

Solving
13 + -3p = 0

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

Add '-13' to each side of the equation.
13 + -13 + -3p = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -3p = 0 + -13
-3p = 0 + -13

Combine like terms: 0 + -13 = -13
-3p = -13

Divide each side by '-3'.
p = 4.333333333

Simplifying
p = 4.333333333
Solution
p = {-4, 4.333333333}