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

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

Simplifying
2(p + 5) + 3p(p + -2) = 2(p + 6)

Reorder the terms:
2(5 + p) + 3p(p + -2) = 2(p + 6)
(5 * 2 + p * 2) + 3p(p + -2) = 2(p + 6)
(10 + 2p) + 3p(p + -2) = 2(p + 6)

Reorder the terms:
10 + 2p + 3p(-2 + p) = 2(p + 6)
10 + 2p + (-2 * 3p + p * 3p) = 2(p + 6)
10 + 2p + (-6p + 3p2) = 2(p + 6)

Combine like terms: 2p + -6p = -4p
10 + -4p + 3p2 = 2(p + 6)

Reorder the terms:
10 + -4p + 3p2 = 2(6 + p)
10 + -4p + 3p2 = (6 * 2 + p * 2)
10 + -4p + 3p2 = (12 + 2p)

Solving
10 + -4p + 3p2 = 12 + 2p

Solving for variable 'p'.

Reorder the terms:
10 + -12 + -4p + -2p + 3p2 = 12 + 2p + -12 + -2p

Combine like terms: 10 + -12 = -2
-2 + -4p + -2p + 3p2 = 12 + 2p + -12 + -2p

Combine like terms: -4p + -2p = -6p
-2 + -6p + 3p2 = 12 + 2p + -12 + -2p

Reorder the terms:
-2 + -6p + 3p2 = 12 + -12 + 2p + -2p

Combine like terms: 12 + -12 = 0
-2 + -6p + 3p2 = 0 + 2p + -2p
-2 + -6p + 3p2 = 2p + -2p

Combine like terms: 2p + -2p = 0
-2 + -6p + 3p2 = 0

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

Divide each side by '3'.
-0.6666666667 + -2p + p2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2p + 0.6666666667 + p2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2p + p2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2p + p2 = 0 + 0.6666666667
-2p + p2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2p + p2 = 0.6666666667

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 = 0.6666666667 + 1

Reorder the terms:
1 + -2p + p2 = 0.6666666667 + 1

Combine like terms: 0.6666666667 + 1 = 1.6666666667
1 + -2p + p2 = 1.6666666667

Factor a perfect square on the left side:
(p + -1)(p + -1) = 1.6666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(p + -1) equal to 1.290994449 and -1.290994449.

Subproblem 1
p + -1 = 1.290994449

Simplifying
p + -1 = 1.290994449

Reorder the terms:
-1 + p = 1.290994449

Solving
-1 + p = 1.290994449

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 = 1.290994449 + 1

Combine like terms: -1 + 1 = 0
0 + p = 1.290994449 + 1
p = 1.290994449 + 1

Combine like terms: 1.290994449 + 1 = 2.290994449
p = 2.290994449

Simplifying
p = 2.290994449

Subproblem 2
p + -1 = -1.290994449

Simplifying
p + -1 = -1.290994449

Reorder the terms:
-1 + p = -1.290994449

Solving
-1 + p = -1.290994449

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 = -1.290994449 + 1

Combine like terms: -1 + 1 = 0
0 + p = -1.290994449 + 1
p = -1.290994449 + 1

Combine like terms: -1.290994449 + 1 = -0.290994449
p = -0.290994449

Simplifying
p = -0.290994449

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.290994449, -0.290994449}