8p-(7p+2)=7(5-p)(3+p)

Solution for 8p-(7p+2)=7(5-p)(3+p) equation:

Simplifying
8p + -1(7p + 2) = 7(5 + -1p)(3 + p)

Reorder the terms:
8p + -1(2 + 7p) = 7(5 + -1p)(3 + p)
8p + (2 * -1 + 7p * -1) = 7(5 + -1p)(3 + p)
8p + (-2 + -7p) = 7(5 + -1p)(3 + p)

Reorder the terms:
-2 + 8p + -7p = 7(5 + -1p)(3 + p)

Combine like terms: 8p + -7p = 1p
-2 + 1p = 7(5 + -1p)(3 + p)

Multiply (5 + -1p) * (3 + p)
-2 + 1p = 7(5(3 + p) + -1p * (3 + p))
-2 + 1p = 7((3 * 5 + p * 5) + -1p * (3 + p))
-2 + 1p = 7((15 + 5p) + -1p * (3 + p))
-2 + 1p = 7(15 + 5p + (3 * -1p + p * -1p))
-2 + 1p = 7(15 + 5p + (-3p + -1p2))

Combine like terms: 5p + -3p = 2p
-2 + 1p = 7(15 + 2p + -1p2)
-2 + 1p = (15 * 7 + 2p * 7 + -1p2 * 7)
-2 + 1p = (105 + 14p + -7p2)

Solving
-2 + 1p = 105 + 14p + -7p2

Solving for variable 'p'.

Reorder the terms:
-2 + -105 + 1p + -14p + 7p2 = 105 + 14p + -7p2 + -105 + -14p + 7p2

Combine like terms: -2 + -105 = -107
-107 + 1p + -14p + 7p2 = 105 + 14p + -7p2 + -105 + -14p + 7p2

Combine like terms: 1p + -14p = -13p
-107 + -13p + 7p2 = 105 + 14p + -7p2 + -105 + -14p + 7p2

Reorder the terms:
-107 + -13p + 7p2 = 105 + -105 + 14p + -14p + -7p2 + 7p2

Combine like terms: 105 + -105 = 0
-107 + -13p + 7p2 = 0 + 14p + -14p + -7p2 + 7p2
-107 + -13p + 7p2 = 14p + -14p + -7p2 + 7p2

Combine like terms: 14p + -14p = 0
-107 + -13p + 7p2 = 0 + -7p2 + 7p2
-107 + -13p + 7p2 = -7p2 + 7p2

Combine like terms: -7p2 + 7p2 = 0
-107 + -13p + 7p2 = 0

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

Divide each side by '7'.
-15.28571429 + -1.857142857p + p2 = 0

Move the constant term to the right:

Add '15.28571429' to each side of the equation.
-15.28571429 + -1.857142857p + 15.28571429 + p2 = 0 + 15.28571429

Reorder the terms:
-15.28571429 + 15.28571429 + -1.857142857p + p2 = 0 + 15.28571429

Combine like terms: -15.28571429 + 15.28571429 = 0.00000000
0.00000000 + -1.857142857p + p2 = 0 + 15.28571429
-1.857142857p + p2 = 0 + 15.28571429

Combine like terms: 0 + 15.28571429 = 15.28571429
-1.857142857p + p2 = 15.28571429

The p term is -1.857142857p.  Take half its coefficient (-0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
-1.857142857p + 0.8622448978 + p2 = 15.28571429 + 0.8622448978

Reorder the terms:
0.8622448978 + -1.857142857p + p2 = 15.28571429 + 0.8622448978

Combine like terms: 15.28571429 + 0.8622448978 = 16.1479591878
0.8622448978 + -1.857142857p + p2 = 16.1479591878

Factor a perfect square on the left side:
(p + -0.9285714285)(p + -0.9285714285) = 16.1479591878

Calculate the square root of the right side: 4.018452337

Break this problem into two subproblems by setting 
(p + -0.9285714285) equal to 4.018452337 and -4.018452337.

Subproblem 1
p + -0.9285714285 = 4.018452337

Simplifying
p + -0.9285714285 = 4.018452337

Reorder the terms:
-0.9285714285 + p = 4.018452337

Solving
-0.9285714285 + p = 4.018452337

Solving for variable 'p'.

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

Add '0.9285714285' to each side of the equation.
-0.9285714285 + 0.9285714285 + p = 4.018452337 + 0.9285714285

Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000
0.0000000000 + p = 4.018452337 + 0.9285714285
p = 4.018452337 + 0.9285714285

Combine like terms: 4.018452337 + 0.9285714285 = 4.9470237655
p = 4.9470237655

Simplifying
p = 4.9470237655

Subproblem 2
p + -0.9285714285 = -4.018452337

Simplifying
p + -0.9285714285 = -4.018452337

Reorder the terms:
-0.9285714285 + p = -4.018452337

Solving
-0.9285714285 + p = -4.018452337

Solving for variable 'p'.

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

Add '0.9285714285' to each side of the equation.
-0.9285714285 + 0.9285714285 + p = -4.018452337 + 0.9285714285

Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000
0.0000000000 + p = -4.018452337 + 0.9285714285
p = -4.018452337 + 0.9285714285

Combine like terms: -4.018452337 + 0.9285714285 = -3.0898809085
p = -3.0898809085

Simplifying
p = -3.0898809085

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.9470237655, -3.0898809085}