-3p(4p-8)+9p-5=-2

Solution for -3p(4p-8)+9p-5=-2 equation:

Simplifying
-3p(4p + -8) + 9p + -5 = -2

Reorder the terms:
-3p(-8 + 4p) + 9p + -5 = -2
(-8 * -3p + 4p * -3p) + 9p + -5 = -2
(24p + -12p2) + 9p + -5 = -2

Reorder the terms:
-5 + 24p + 9p + -12p2 = -2

Combine like terms: 24p + 9p = 33p
-5 + 33p + -12p2 = -2

Solving
-5 + 33p + -12p2 = -2

Solving for variable 'p'.

Reorder the terms:
-5 + 2 + 33p + -12p2 = -2 + 2

Combine like terms: -5 + 2 = -3
-3 + 33p + -12p2 = -2 + 2

Combine like terms: -2 + 2 = 0
-3 + 33p + -12p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 11p + -4p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 11p + -4p2)' equal to zero and attempt to solve:

Simplifying
-1 + 11p + -4p2 = 0

Solving
-1 + 11p + -4p2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
0.25 + -2.75p + p2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2.75p + -0.25 + p2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2.75p + p2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2.75p + p2 = 0 + -0.25
-2.75p + p2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2.75p + p2 = -0.25

The p term is -2.75p.  Take half its coefficient (-1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
-2.75p + 1.890625 + p2 = -0.25 + 1.890625

Reorder the terms:
1.890625 + -2.75p + p2 = -0.25 + 1.890625

Combine like terms: -0.25 + 1.890625 = 1.640625
1.890625 + -2.75p + p2 = 1.640625

Factor a perfect square on the left side:
(p + -1.375)(p + -1.375) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(p + -1.375) equal to 1.280868846 and -1.280868846.

Subproblem 1
p + -1.375 = 1.280868846

Simplifying
p + -1.375 = 1.280868846

Reorder the terms:
-1.375 + p = 1.280868846

Solving
-1.375 + p = 1.280868846

Solving for variable 'p'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + p = 1.280868846 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + p = 1.280868846 + 1.375
p = 1.280868846 + 1.375

Combine like terms: 1.280868846 + 1.375 = 2.655868846
p = 2.655868846

Simplifying
p = 2.655868846

Subproblem 2
p + -1.375 = -1.280868846

Simplifying
p + -1.375 = -1.280868846

Reorder the terms:
-1.375 + p = -1.280868846

Solving
-1.375 + p = -1.280868846

Solving for variable 'p'.

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

Add '1.375' to each side of the equation.
-1.375 + 1.375 + p = -1.280868846 + 1.375

Combine like terms: -1.375 + 1.375 = 0.000
0.000 + p = -1.280868846 + 1.375
p = -1.280868846 + 1.375

Combine like terms: -1.280868846 + 1.375 = 0.094131154
p = 0.094131154

Simplifying
p = 0.094131154

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.655868846, 0.094131154}
Solution
p = {2.655868846, 0.094131154}