105=(p^2-p)

Solution for 105=(p^2-p) equation:

Simplifying
105 = (p2 + -1p)

Reorder the terms:
105 = (-1p + p2)

Remove parenthesis around (-1p + p2)
105 = -1p + p2

Solving
105 = -1p + p2

Solving for variable 'p'.

Reorder the terms:
105 + p + -1p2 = -1p + p + p2 + -1p2

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

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

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

Divide each side by '-1'.
-105 + -1p + p2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + -1p + 105 + p2 = 0 + 105

Reorder the terms:
-105 + 105 + -1p + p2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + -1p + p2 = 0 + 105
-1p + p2 = 0 + 105

Combine like terms: 0 + 105 = 105
-1p + p2 = 105

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1p + 0.25 + p2 = 105 + 0.25

Reorder the terms:
0.25 + -1p + p2 = 105 + 0.25

Combine like terms: 105 + 0.25 = 105.25
0.25 + -1p + p2 = 105.25

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 105.25

Calculate the square root of the right side: 10.259142264

Break this problem into two subproblems by setting 
(p + 0.5) equal to 10.259142264 and -10.259142264.

Subproblem 1
p + 0.5 = 10.259142264

Simplifying
p + 0.5 = 10.259142264

Reorder the terms:
0.5 + p = 10.259142264

Solving
0.5 + p = 10.259142264

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 10.259142264 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 10.259142264 + -0.5
p = 10.259142264 + -0.5

Combine like terms: 10.259142264 + -0.5 = 9.759142264
p = 9.759142264

Simplifying
p = 9.759142264

Subproblem 2
p + 0.5 = -10.259142264

Simplifying
p + 0.5 = -10.259142264

Reorder the terms:
0.5 + p = -10.259142264

Solving
0.5 + p = -10.259142264

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -10.259142264 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -10.259142264 + -0.5
p = -10.259142264 + -0.5

Combine like terms: -10.259142264 + -0.5 = -10.759142264
p = -10.759142264

Simplifying
p = -10.759142264

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {9.759142264, -10.759142264}