(P+3)(P+3)=81

Solution for (P+3)(P+3)=81 equation:

Simplifying
(P + 3)(P + 3) = 81

Reorder the terms:
(3 + P)(P + 3) = 81

Reorder the terms:
(3 + P)(3 + P) = 81

Multiply (3 + P) * (3 + P)
(3(3 + P) + P(3 + P)) = 81
((3 * 3 + P * 3) + P(3 + P)) = 81
((9 + 3P) + P(3 + P)) = 81
(9 + 3P + (3 * P + P * P)) = 81
(9 + 3P + (3P + P2)) = 81

Combine like terms: 3P + 3P = 6P
(9 + 6P + P2) = 81

Solving
9 + 6P + P2 = 81

Solving for variable 'P'.

Reorder the terms:
9 + -81 + 6P + P2 = 81 + -81

Combine like terms: 9 + -81 = -72
-72 + 6P + P2 = 81 + -81

Combine like terms: 81 + -81 = 0
-72 + 6P + P2 = 0

Factor a trinomial.
(-12 + -1P)(6 + -1P) = 0

Subproblem 1
Set the factor '(-12 + -1P)' equal to zero and attempt to solve:

Simplifying
-12 + -1P = 0

Solving
-12 + -1P = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1P = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1P = 0 + 12
-1P = 0 + 12

Combine like terms: 0 + 12 = 12
-1P = 12

Divide each side by '-1'.
P = -12

Simplifying
P = -12
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 = {-12, 6}