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

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

Simplifying
-2(3p + 5) * 8p = 5p + 8

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

Reorder the terms for easier multiplication:
-2 * 8p(5 + 3p) = 5p + 8

Multiply -2 * 8
-16p(5 + 3p) = 5p + 8
(5 * -16p + 3p * -16p) = 5p + 8
(-80p + -48p2) = 5p + 8

Reorder the terms:
-80p + -48p2 = 8 + 5p

Solving
-80p + -48p2 = 8 + 5p

Solving for variable 'p'.

Reorder the terms:
-8 + -80p + -5p + -48p2 = 8 + 5p + -8 + -5p

Combine like terms: -80p + -5p = -85p
-8 + -85p + -48p2 = 8 + 5p + -8 + -5p

Reorder the terms:
-8 + -85p + -48p2 = 8 + -8 + 5p + -5p

Combine like terms: 8 + -8 = 0
-8 + -85p + -48p2 = 0 + 5p + -5p
-8 + -85p + -48p2 = 5p + -5p

Combine like terms: 5p + -5p = 0
-8 + -85p + -48p2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 85p + 48p2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + 85p + 48p2)' equal to zero and attempt to solve:

Simplifying
8 + 85p + 48p2 = 0

Solving
8 + 85p + 48p2 = 0

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

Divide each side by '48'.
0.1666666667 + 1.770833333p + p2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 1.770833333p + -0.1666666667 + p2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 1.770833333p + p2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 1.770833333p + p2 = 0 + -0.1666666667
1.770833333p + p2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
1.770833333p + p2 = -0.1666666667

The p term is 1.770833333p.  Take half its coefficient (0.8854166665).
Square it (0.7839626733) and add it to both sides.

Add '0.7839626733' to each side of the equation.
1.770833333p + 0.7839626733 + p2 = -0.1666666667 + 0.7839626733

Reorder the terms:
0.7839626733 + 1.770833333p + p2 = -0.1666666667 + 0.7839626733

Combine like terms: -0.1666666667 + 0.7839626733 = 0.6172960066
0.7839626733 + 1.770833333p + p2 = 0.6172960066

Factor a perfect square on the left side:
(p + 0.8854166665)(p + 0.8854166665) = 0.6172960066

Calculate the square root of the right side: 0.785681874

Break this problem into two subproblems by setting 
(p + 0.8854166665) equal to 0.785681874 and -0.785681874.

Subproblem 1
p + 0.8854166665 = 0.785681874

Simplifying
p + 0.8854166665 = 0.785681874

Reorder the terms:
0.8854166665 + p = 0.785681874

Solving
0.8854166665 + p = 0.785681874

Solving for variable 'p'.

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

Add '-0.8854166665' to each side of the equation.
0.8854166665 + -0.8854166665 + p = 0.785681874 + -0.8854166665

Combine like terms: 0.8854166665 + -0.8854166665 = 0.0000000000
0.0000000000 + p = 0.785681874 + -0.8854166665
p = 0.785681874 + -0.8854166665

Combine like terms: 0.785681874 + -0.8854166665 = -0.0997347925
p = -0.0997347925

Simplifying
p = -0.0997347925

Subproblem 2
p + 0.8854166665 = -0.785681874

Simplifying
p + 0.8854166665 = -0.785681874

Reorder the terms:
0.8854166665 + p = -0.785681874

Solving
0.8854166665 + p = -0.785681874

Solving for variable 'p'.

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

Add '-0.8854166665' to each side of the equation.
0.8854166665 + -0.8854166665 + p = -0.785681874 + -0.8854166665

Combine like terms: 0.8854166665 + -0.8854166665 = 0.0000000000
0.0000000000 + p = -0.785681874 + -0.8854166665
p = -0.785681874 + -0.8854166665

Combine like terms: -0.785681874 + -0.8854166665 = -1.6710985405
p = -1.6710985405

Simplifying
p = -1.6710985405

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-0.0997347925, -1.6710985405}
Solution
p = {-0.0997347925, -1.6710985405}