p^2=14p-33

Solution for p^2=14p-33 equation:

Simplifying
p2 = 14p + -33

Reorder the terms:
p2 = -33 + 14p

Solving
p2 = -33 + 14p

Solving for variable 'p'.

Reorder the terms:
33 + -14p + p2 = -33 + 14p + 33 + -14p

Reorder the terms:
33 + -14p + p2 = -33 + 33 + 14p + -14p

Combine like terms: -33 + 33 = 0
33 + -14p + p2 = 0 + 14p + -14p
33 + -14p + p2 = 14p + -14p

Combine like terms: 14p + -14p = 0
33 + -14p + p2 = 0

Factor a trinomial.
(3 + -1p)(11 + -1p) = 0

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

Simplifying
3 + -1p = 0

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

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

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

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Subproblem 2
Set the factor '(11 + -1p)' equal to zero and attempt to solve:

Simplifying
11 + -1p = 0

Solving
11 + -1p = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1p = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1p = 0 + -11
-1p = 0 + -11

Combine like terms: 0 + -11 = -11
-1p = -11

Divide each side by '-1'.
p = 11

Simplifying
p = 11
Solution
p = {3, 11}