3=P(6+P)

Solution for 3=P(6+P) equation:

Simplifying
3 = P(6 + P)
3 = (6 * P + P * P)
3 = (6P + P2)

Solving
3 = 6P + P2

Solving for variable 'P'.

Reorder the terms:
3 + -6P + -1P2 = 6P + -6P + P2 + -1P2

Combine like terms: 6P + -6P = 0
3 + -6P + -1P2 = 0 + P2 + -1P2
3 + -6P + -1P2 = P2 + -1P2

Combine like terms: P2 + -1P2 = 0
3 + -6P + -1P2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 6P + P2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6P + 3 + P2 = 0 + 3

Reorder the terms:
-3 + 3 + 6P + P2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6P + P2 = 0 + 3
6P + P2 = 0 + 3

Combine like terms: 0 + 3 = 3
6P + P2 = 3

The P term is 6P.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6P + 9 + P2 = 3 + 9

Reorder the terms:
9 + 6P + P2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6P + P2 = 12

Factor a perfect square on the left side:
(P + 3)(P + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(P + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
P + 3 = 3.464101615

Simplifying
P + 3 = 3.464101615

Reorder the terms:
3 + P = 3.464101615

Solving
3 + P = 3.464101615

Solving for variable 'P'.

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

Add '-3' to each side of the equation.
3 + -3 + P = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + P = 3.464101615 + -3
P = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
P = 0.464101615

Simplifying
P = 0.464101615

Subproblem 2
P + 3 = -3.464101615

Simplifying
P + 3 = -3.464101615

Reorder the terms:
3 + P = -3.464101615

Solving
3 + P = -3.464101615

Solving for variable 'P'.

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

Add '-3' to each side of the equation.
3 + -3 + P = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + P = -3.464101615 + -3
P = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
P = -6.464101615

Simplifying
P = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
P = {0.464101615, -6.464101615}