4p^2-24p-8=0

Solution for 4p^2-24p-8=0 equation:

Simplifying
4p2 + -24p + -8 = 0

Reorder the terms:
-8 + -24p + 4p2 = 0

Solving
-8 + -24p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -6p + p2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -6p + p2)' equal to zero and attempt to solve:

Simplifying
-2 + -6p + p2 = 0

Solving
-2 + -6p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -6p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + -6p + p2 = 0 + 2

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

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

The p term is -6p.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6p + 9 + p2 = 2 + 9

Reorder the terms:
9 + -6p + p2 = 2 + 9

Combine like terms: 2 + 9 = 11
9 + -6p + p2 = 11

Factor a perfect square on the left side:
(p + -3)(p + -3) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(p + -3) equal to 3.31662479 and -3.31662479.

Subproblem 1
p + -3 = 3.31662479

Simplifying
p + -3 = 3.31662479

Reorder the terms:
-3 + p = 3.31662479

Solving
-3 + p = 3.31662479

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + p = 3.31662479 + 3

Combine like terms: -3 + 3 = 0
0 + p = 3.31662479 + 3
p = 3.31662479 + 3

Combine like terms: 3.31662479 + 3 = 6.31662479
p = 6.31662479

Simplifying
p = 6.31662479

Subproblem 2
p + -3 = -3.31662479

Simplifying
p + -3 = -3.31662479

Reorder the terms:
-3 + p = -3.31662479

Solving
-3 + p = -3.31662479

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + p = -3.31662479 + 3

Combine like terms: -3 + 3 = 0
0 + p = -3.31662479 + 3
p = -3.31662479 + 3

Combine like terms: -3.31662479 + 3 = -0.31662479
p = -0.31662479

Simplifying
p = -0.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.31662479, -0.31662479}
Solution
p = {6.31662479, -0.31662479}