3(p^2+2p+1)=81

Solution for 3(p^2+2p+1)=81 equation:

Simplifying
3(p2 + 2p + 1) = 81

Reorder the terms:
3(1 + 2p + p2) = 81
(1 * 3 + 2p * 3 + p2 * 3) = 81
(3 + 6p + 3p2) = 81

Solving
3 + 6p + 3p2 = 81

Solving for variable 'p'.

Reorder the terms:
3 + -81 + 6p + 3p2 = 81 + -81

Combine like terms: 3 + -81 = -78
-78 + 6p + 3p2 = 81 + -81

Combine like terms: 81 + -81 = 0
-78 + 6p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-26 + 2p + p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-26 + 2p + p2)' equal to zero and attempt to solve:

Simplifying
-26 + 2p + p2 = 0

Solving
-26 + 2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 2p + 26 + p2 = 0 + 26

Reorder the terms:
-26 + 26 + 2p + p2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 2p + p2 = 0 + 26
2p + p2 = 0 + 26

Combine like terms: 0 + 26 = 26
2p + p2 = 26

The p term is 2p.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2p + 1 + p2 = 26 + 1

Reorder the terms:
1 + 2p + p2 = 26 + 1

Combine like terms: 26 + 1 = 27
1 + 2p + p2 = 27

Factor a perfect square on the left side:
(p + 1)(p + 1) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(p + 1) equal to 5.196152423 and -5.196152423.

Subproblem 1
p + 1 = 5.196152423

Simplifying
p + 1 = 5.196152423

Reorder the terms:
1 + p = 5.196152423

Solving
1 + p = 5.196152423

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = 5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + p = 5.196152423 + -1
p = 5.196152423 + -1

Combine like terms: 5.196152423 + -1 = 4.196152423
p = 4.196152423

Simplifying
p = 4.196152423

Subproblem 2
p + 1 = -5.196152423

Simplifying
p + 1 = -5.196152423

Reorder the terms:
1 + p = -5.196152423

Solving
1 + p = -5.196152423

Solving for variable 'p'.

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

Add '-1' to each side of the equation.
1 + -1 + p = -5.196152423 + -1

Combine like terms: 1 + -1 = 0
0 + p = -5.196152423 + -1
p = -5.196152423 + -1

Combine like terms: -5.196152423 + -1 = -6.196152423
p = -6.196152423

Simplifying
p = -6.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.196152423, -6.196152423}
Solution
p = {4.196152423, -6.196152423}