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

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

Simplifying
3p + -8 = 2(p + 8) * 3p

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

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

Reorder the terms for easier multiplication:
-8 + 3p = 2 * 3p(8 + p)

Multiply 2 * 3
-8 + 3p = 6p(8 + p)
-8 + 3p = (8 * 6p + p * 6p)
-8 + 3p = (48p + 6p2)

Solving
-8 + 3p = 48p + 6p2

Solving for variable 'p'.

Combine like terms: 3p + -48p = -45p
-8 + -45p + -6p2 = 48p + 6p2 + -48p + -6p2

Reorder the terms:
-8 + -45p + -6p2 = 48p + -48p + 6p2 + -6p2

Combine like terms: 48p + -48p = 0
-8 + -45p + -6p2 = 0 + 6p2 + -6p2
-8 + -45p + -6p2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
-8 + -45p + -6p2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 45p + 6p2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + 45p + 6p2)' equal to zero and attempt to solve:

Simplifying
8 + 45p + 6p2 = 0

Solving
8 + 45p + 6p2 = 0

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

Divide each side by '6'.
1.333333333 + 7.5p + p2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 7.5p + -1.333333333 + p2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 7.5p + p2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 7.5p + p2 = 0 + -1.333333333
7.5p + p2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
7.5p + p2 = -1.333333333

The p term is 7.5p.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5p + 14.0625 + p2 = -1.333333333 + 14.0625

Reorder the terms:
14.0625 + 7.5p + p2 = -1.333333333 + 14.0625

Combine like terms: -1.333333333 + 14.0625 = 12.729166667
14.0625 + 7.5p + p2 = 12.729166667

Factor a perfect square on the left side:
(p + 3.75)(p + 3.75) = 12.729166667

Calculate the square root of the right side: 3.567795771

Break this problem into two subproblems by setting 
(p + 3.75) equal to 3.567795771 and -3.567795771.

Subproblem 1
p + 3.75 = 3.567795771

Simplifying
p + 3.75 = 3.567795771

Reorder the terms:
3.75 + p = 3.567795771

Solving
3.75 + p = 3.567795771

Solving for variable 'p'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + p = 3.567795771 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + p = 3.567795771 + -3.75
p = 3.567795771 + -3.75

Combine like terms: 3.567795771 + -3.75 = -0.182204229
p = -0.182204229

Simplifying
p = -0.182204229

Subproblem 2
p + 3.75 = -3.567795771

Simplifying
p + 3.75 = -3.567795771

Reorder the terms:
3.75 + p = -3.567795771

Solving
3.75 + p = -3.567795771

Solving for variable 'p'.

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

Add '-3.75' to each side of the equation.
3.75 + -3.75 + p = -3.567795771 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + p = -3.567795771 + -3.75
p = -3.567795771 + -3.75

Combine like terms: -3.567795771 + -3.75 = -7.317795771
p = -7.317795771

Simplifying
p = -7.317795771

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.182204229, -7.317795771}
Solution
p = {-0.182204229, -7.317795771}