-3p^2-6p+5=0

Solution for -3p^2-6p+5=0 equation:

Simplifying
-3p2 + -6p + 5 = 0

Reorder the terms:
5 + -6p + -3p2 = 0

Solving
5 + -6p + -3p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-1.666666667 + 2p + p2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 2p + 1.666666667 + p2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 2p + p2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 2p + p2 = 0 + 1.666666667
2p + p2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
2p + p2 = 1.666666667

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 = 1.666666667 + 1

Reorder the terms:
1 + 2p + p2 = 1.666666667 + 1

Combine like terms: 1.666666667 + 1 = 2.666666667
1 + 2p + p2 = 2.666666667

Factor a perfect square on the left side:
(p + 1)(p + 1) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(p + 1) equal to 1.632993162 and -1.632993162.

Subproblem 1
p + 1 = 1.632993162

Simplifying
p + 1 = 1.632993162

Reorder the terms:
1 + p = 1.632993162

Solving
1 + p = 1.632993162

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 = 1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + p = 1.632993162 + -1
p = 1.632993162 + -1

Combine like terms: 1.632993162 + -1 = 0.632993162
p = 0.632993162

Simplifying
p = 0.632993162

Subproblem 2
p + 1 = -1.632993162

Simplifying
p + 1 = -1.632993162

Reorder the terms:
1 + p = -1.632993162

Solving
1 + p = -1.632993162

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 = -1.632993162 + -1

Combine like terms: 1 + -1 = 0
0 + p = -1.632993162 + -1
p = -1.632993162 + -1

Combine like terms: -1.632993162 + -1 = -2.632993162
p = -2.632993162

Simplifying
p = -2.632993162

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.632993162, -2.632993162}