-p^2+6p+3=0

Solution for -p^2+6p+3=0 equation:

Simplifying
-1p2 + 6p + 3 = 0

Reorder the terms:
3 + 6p + -1p2 = 0

Solving
3 + 6p + -1p2 = 0

Solving for variable 'p'.

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 = 6.464101615
p = 6.464101615

Simplifying
p = 6.464101615

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 = -0.464101615
p = -0.464101615

Simplifying
p = -0.464101615

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