40p^2-420p-40=0

Solution for 40p^2-420p-40=0 equation:

Simplifying
40p2 + -420p + -40 = 0

Reorder the terms:
-40 + -420p + 40p2 = 0

Solving
-40 + -420p + 40p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-2 + -21p + 2p2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-2 + -21p + 2p2)' equal to zero and attempt to solve:

Simplifying
-2 + -21p + 2p2 = 0

Solving
-2 + -21p + 2p2 = 0

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

Divide each side by '2'.
-1 + -10.5p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -10.5p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + -10.5p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -10.5p + p2 = 0 + 1
-10.5p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
-10.5p + p2 = 1

The p term is -10.5p.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5p + 27.5625 + p2 = 1 + 27.5625

Reorder the terms:
27.5625 + -10.5p + p2 = 1 + 27.5625

Combine like terms: 1 + 27.5625 = 28.5625
27.5625 + -10.5p + p2 = 28.5625

Factor a perfect square on the left side:
(p + -5.25)(p + -5.25) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(p + -5.25) equal to 5.344389582 and -5.344389582.

Subproblem 1
p + -5.25 = 5.344389582

Simplifying
p + -5.25 = 5.344389582

Reorder the terms:
-5.25 + p = 5.344389582

Solving
-5.25 + p = 5.344389582

Solving for variable 'p'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + p = 5.344389582 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + p = 5.344389582 + 5.25
p = 5.344389582 + 5.25

Combine like terms: 5.344389582 + 5.25 = 10.594389582
p = 10.594389582

Simplifying
p = 10.594389582

Subproblem 2
p + -5.25 = -5.344389582

Simplifying
p + -5.25 = -5.344389582

Reorder the terms:
-5.25 + p = -5.344389582

Solving
-5.25 + p = -5.344389582

Solving for variable 'p'.

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

Add '5.25' to each side of the equation.
-5.25 + 5.25 + p = -5.344389582 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + p = -5.344389582 + 5.25
p = -5.344389582 + 5.25

Combine like terms: -5.344389582 + 5.25 = -0.094389582
p = -0.094389582

Simplifying
p = -0.094389582

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {10.594389582, -0.094389582}
Solution
p = {10.594389582, -0.094389582}