6(p^2-2p-1)=5p

Solution for 6(p^2-2p-1)=5p equation:

Simplifying
6(p2 + -2p + -1) = 5p

Reorder the terms:
6(-1 + -2p + p2) = 5p
(-1 * 6 + -2p * 6 + p2 * 6) = 5p
(-6 + -12p + 6p2) = 5p

Solving
-6 + -12p + 6p2 = 5p

Solving for variable 'p'.

Reorder the terms:
-6 + -12p + -5p + 6p2 = 5p + -5p

Combine like terms: -12p + -5p = -17p
-6 + -17p + 6p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
-6 + -17p + 6p2 = 0

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

Divide each side by '6'.
-1 + -2.833333333p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.833333333p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.833333333p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.833333333p + p2 = 0 + 1
-2.833333333p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.833333333p + p2 = 1

The p term is -2.833333333p.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333p + 2.006944445 + p2 = 1 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333p + p2 = 1 + 2.006944445

Combine like terms: 1 + 2.006944445 = 3.006944445
2.006944445 + -2.833333333p + p2 = 3.006944445

Factor a perfect square on the left side:
(p + -1.416666667)(p + -1.416666667) = 3.006944445

Calculate the square root of the right side: 1.734054337

Break this problem into two subproblems by setting 
(p + -1.416666667) equal to 1.734054337 and -1.734054337.

Subproblem 1
p + -1.416666667 = 1.734054337

Simplifying
p + -1.416666667 = 1.734054337

Reorder the terms:
-1.416666667 + p = 1.734054337

Solving
-1.416666667 + p = 1.734054337

Solving for variable 'p'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + p = 1.734054337 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + p = 1.734054337 + 1.416666667
p = 1.734054337 + 1.416666667

Combine like terms: 1.734054337 + 1.416666667 = 3.150721004
p = 3.150721004

Simplifying
p = 3.150721004

Subproblem 2
p + -1.416666667 = -1.734054337

Simplifying
p + -1.416666667 = -1.734054337

Reorder the terms:
-1.416666667 + p = -1.734054337

Solving
-1.416666667 + p = -1.734054337

Solving for variable 'p'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + p = -1.734054337 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + p = -1.734054337 + 1.416666667
p = -1.734054337 + 1.416666667

Combine like terms: -1.734054337 + 1.416666667 = -0.31738767
p = -0.31738767

Simplifying
p = -0.31738767

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.150721004, -0.31738767}