-2p(17p-5)+8(5p+2)=p-(3p+6)

Solution for -2p(17p-5)+8(5p+2)=p-(3p+6) equation:

Simplifying
-2p(17p + -5) + 8(5p + 2) = p + -1(3p + 6)

Reorder the terms:
-2p(-5 + 17p) + 8(5p + 2) = p + -1(3p + 6)
(-5 * -2p + 17p * -2p) + 8(5p + 2) = p + -1(3p + 6)
(10p + -34p2) + 8(5p + 2) = p + -1(3p + 6)

Reorder the terms:
10p + -34p2 + 8(2 + 5p) = p + -1(3p + 6)
10p + -34p2 + (2 * 8 + 5p * 8) = p + -1(3p + 6)
10p + -34p2 + (16 + 40p) = p + -1(3p + 6)

Reorder the terms:
16 + 10p + 40p + -34p2 = p + -1(3p + 6)

Combine like terms: 10p + 40p = 50p
16 + 50p + -34p2 = p + -1(3p + 6)

Reorder the terms:
16 + 50p + -34p2 = p + -1(6 + 3p)
16 + 50p + -34p2 = p + (6 * -1 + 3p * -1)
16 + 50p + -34p2 = p + (-6 + -3p)

Reorder the terms:
16 + 50p + -34p2 = -6 + p + -3p

Combine like terms: p + -3p = -2p
16 + 50p + -34p2 = -6 + -2p

Solving
16 + 50p + -34p2 = -6 + -2p

Solving for variable 'p'.

Reorder the terms:
16 + 6 + 50p + 2p + -34p2 = -6 + -2p + 6 + 2p

Combine like terms: 16 + 6 = 22
22 + 50p + 2p + -34p2 = -6 + -2p + 6 + 2p

Combine like terms: 50p + 2p = 52p
22 + 52p + -34p2 = -6 + -2p + 6 + 2p

Reorder the terms:
22 + 52p + -34p2 = -6 + 6 + -2p + 2p

Combine like terms: -6 + 6 = 0
22 + 52p + -34p2 = 0 + -2p + 2p
22 + 52p + -34p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
22 + 52p + -34p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(11 + 26p + -17p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(11 + 26p + -17p2)' equal to zero and attempt to solve:

Simplifying
11 + 26p + -17p2 = 0

Solving
11 + 26p + -17p2 = 0

Begin completing the square.  Divide all terms by
-17 the coefficient of the squared term: 

Divide each side by '-17'.
-0.6470588235 + -1.529411765p + p2 = 0

Move the constant term to the right:

Add '0.6470588235' to each side of the equation.
-0.6470588235 + -1.529411765p + 0.6470588235 + p2 = 0 + 0.6470588235

Reorder the terms:
-0.6470588235 + 0.6470588235 + -1.529411765p + p2 = 0 + 0.6470588235

Combine like terms: -0.6470588235 + 0.6470588235 = 0.0000000000
0.0000000000 + -1.529411765p + p2 = 0 + 0.6470588235
-1.529411765p + p2 = 0 + 0.6470588235

Combine like terms: 0 + 0.6470588235 = 0.6470588235
-1.529411765p + p2 = 0.6470588235

The p term is -1.529411765p.  Take half its coefficient (-0.7647058825).
Square it (0.5847750867) and add it to both sides.

Add '0.5847750867' to each side of the equation.
-1.529411765p + 0.5847750867 + p2 = 0.6470588235 + 0.5847750867

Reorder the terms:
0.5847750867 + -1.529411765p + p2 = 0.6470588235 + 0.5847750867

Combine like terms: 0.6470588235 + 0.5847750867 = 1.2318339102
0.5847750867 + -1.529411765p + p2 = 1.2318339102

Factor a perfect square on the left side:
(p + -0.7647058825)(p + -0.7647058825) = 1.2318339102

Calculate the square root of the right side: 1.109880133

Break this problem into two subproblems by setting 
(p + -0.7647058825) equal to 1.109880133 and -1.109880133.

Subproblem 1
p + -0.7647058825 = 1.109880133

Simplifying
p + -0.7647058825 = 1.109880133

Reorder the terms:
-0.7647058825 + p = 1.109880133

Solving
-0.7647058825 + p = 1.109880133

Solving for variable 'p'.

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

Add '0.7647058825' to each side of the equation.
-0.7647058825 + 0.7647058825 + p = 1.109880133 + 0.7647058825

Combine like terms: -0.7647058825 + 0.7647058825 = 0.0000000000
0.0000000000 + p = 1.109880133 + 0.7647058825
p = 1.109880133 + 0.7647058825

Combine like terms: 1.109880133 + 0.7647058825 = 1.8745860155
p = 1.8745860155

Simplifying
p = 1.8745860155

Subproblem 2
p + -0.7647058825 = -1.109880133

Simplifying
p + -0.7647058825 = -1.109880133

Reorder the terms:
-0.7647058825 + p = -1.109880133

Solving
-0.7647058825 + p = -1.109880133

Solving for variable 'p'.

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

Add '0.7647058825' to each side of the equation.
-0.7647058825 + 0.7647058825 + p = -1.109880133 + 0.7647058825

Combine like terms: -0.7647058825 + 0.7647058825 = 0.0000000000
0.0000000000 + p = -1.109880133 + 0.7647058825
p = -1.109880133 + 0.7647058825

Combine like terms: -1.109880133 + 0.7647058825 = -0.3451742505
p = -0.3451742505

Simplifying
p = -0.3451742505

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.8745860155, -0.3451742505}
Solution
p = {1.8745860155, -0.3451742505}