3(p-9)(p-9)=81

Solution for 3(p-9)(p-9)=81 equation:

Simplifying
3(p + -9)(p + -9) = 81

Reorder the terms:
3(-9 + p)(p + -9) = 81

Reorder the terms:
3(-9 + p)(-9 + p) = 81

Multiply (-9 + p) * (-9 + p)
3(-9(-9 + p) + p(-9 + p)) = 81
3((-9 * -9 + p * -9) + p(-9 + p)) = 81
3((81 + -9p) + p(-9 + p)) = 81
3(81 + -9p + (-9 * p + p * p)) = 81
3(81 + -9p + (-9p + p2)) = 81

Combine like terms: -9p + -9p = -18p
3(81 + -18p + p2) = 81
(81 * 3 + -18p * 3 + p2 * 3) = 81
(243 + -54p + 3p2) = 81

Solving
243 + -54p + 3p2 = 81

Solving for variable 'p'.

Reorder the terms:
243 + -81 + -54p + 3p2 = 81 + -81

Combine like terms: 243 + -81 = 162
162 + -54p + 3p2 = 81 + -81

Combine like terms: 81 + -81 = 0
162 + -54p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(54 + -18p + p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(54 + -18p + p2)' equal to zero and attempt to solve:

Simplifying
54 + -18p + p2 = 0

Solving
54 + -18p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-54' to each side of the equation.
54 + -18p + -54 + p2 = 0 + -54

Reorder the terms:
54 + -54 + -18p + p2 = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -18p + p2 = 0 + -54
-18p + p2 = 0 + -54

Combine like terms: 0 + -54 = -54
-18p + p2 = -54

The p term is -18p.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18p + 81 + p2 = -54 + 81

Reorder the terms:
81 + -18p + p2 = -54 + 81

Combine like terms: -54 + 81 = 27
81 + -18p + p2 = 27

Factor a perfect square on the left side:
(p + -9)(p + -9) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(p + -9) equal to 5.196152423 and -5.196152423.

Subproblem 1
p + -9 = 5.196152423

Simplifying
p + -9 = 5.196152423

Reorder the terms:
-9 + p = 5.196152423

Solving
-9 + p = 5.196152423

Solving for variable 'p'.

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

Add '9' to each side of the equation.
-9 + 9 + p = 5.196152423 + 9

Combine like terms: -9 + 9 = 0
0 + p = 5.196152423 + 9
p = 5.196152423 + 9

Combine like terms: 5.196152423 + 9 = 14.196152423
p = 14.196152423

Simplifying
p = 14.196152423

Subproblem 2
p + -9 = -5.196152423

Simplifying
p + -9 = -5.196152423

Reorder the terms:
-9 + p = -5.196152423

Solving
-9 + p = -5.196152423

Solving for variable 'p'.

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

Add '9' to each side of the equation.
-9 + 9 + p = -5.196152423 + 9

Combine like terms: -9 + 9 = 0
0 + p = -5.196152423 + 9
p = -5.196152423 + 9

Combine like terms: -5.196152423 + 9 = 3.803847577
p = 3.803847577

Simplifying
p = 3.803847577

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {14.196152423, 3.803847577}
Solution
p = {14.196152423, 3.803847577}