p^2-21=2p+3

Solution for p^2-21=2p+3 equation:

Simplifying
p2 + -21 = 2p + 3

Reorder the terms:
-21 + p2 = 2p + 3

Reorder the terms:
-21 + p2 = 3 + 2p

Solving
-21 + p2 = 3 + 2p

Solving for variable 'p'.

Reorder the terms:
-21 + -3 + -2p + p2 = 3 + 2p + -3 + -2p

Combine like terms: -21 + -3 = -24
-24 + -2p + p2 = 3 + 2p + -3 + -2p

Reorder the terms:
-24 + -2p + p2 = 3 + -3 + 2p + -2p

Combine like terms: 3 + -3 = 0
-24 + -2p + p2 = 0 + 2p + -2p
-24 + -2p + p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-24 + -2p + p2 = 0

Factor a trinomial.
(-4 + -1p)(6 + -1p) = 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 '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 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 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {-4, 6}