p^2-72=-14p

Solution for p^2-72=-14p equation:

Simplifying
p2 + -72 = -14p

Reorder the terms:
-72 + p2 = -14p

Solving
-72 + p2 = -14p

Solving for variable 'p'.

Reorder the terms:
-72 + 14p + p2 = -14p + 14p

Combine like terms: -14p + 14p = 0
-72 + 14p + p2 = 0

Factor a trinomial.
(-18 + -1p)(4 + -1p) = 0

Subproblem 1
Set the factor '(-18 + -1p)' equal to zero and attempt to solve:

Simplifying
-18 + -1p = 0

Solving
-18 + -1p = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1p = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1p = 0 + 18
-1p = 0 + 18

Combine like terms: 0 + 18 = 18
-1p = 18

Divide each side by '-1'.
p = -18

Simplifying
p = -18
Subproblem 2
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
Solution
p = {-18, 4}