8*(2p-4)*3p=20

Solution for 8*(2p-4)*3p=20 equation:

Simplifying
8(2p + -4) * 3p = 20

Reorder the terms:
8(-4 + 2p) * 3p = 20

Reorder the terms for easier multiplication:
8 * 3p(-4 + 2p) = 20

Multiply 8 * 3
24p(-4 + 2p) = 20
(-4 * 24p + 2p * 24p) = 20
(-96p + 48p2) = 20

Solving
-96p + 48p2 = 20

Solving for variable 'p'.

Reorder the terms:
-20 + -96p + 48p2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -96p + 48p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -24p + 12p2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -24p + 12p2)' equal to zero and attempt to solve:

Simplifying
-5 + -24p + 12p2 = 0

Solving
-5 + -24p + 12p2 = 0

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

Divide each side by '12'.
-0.4166666667 + -2p + p2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -2p + 0.4166666667 + p2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -2p + p2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -2p + p2 = 0 + 0.4166666667
-2p + p2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-2p + p2 = 0.4166666667

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 0.4166666667 + 1

Reorder the terms:
1 + -2p + p2 = 0.4166666667 + 1

Combine like terms: 0.4166666667 + 1 = 1.4166666667
1 + -2p + p2 = 1.4166666667

Factor a perfect square on the left side:
(p + -1)(p + -1) = 1.4166666667

Calculate the square root of the right side: 1.190238071

Break this problem into two subproblems by setting 
(p + -1) equal to 1.190238071 and -1.190238071.

Subproblem 1
p + -1 = 1.190238071

Simplifying
p + -1 = 1.190238071

Reorder the terms:
-1 + p = 1.190238071

Solving
-1 + p = 1.190238071

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 1.190238071 + 1

Combine like terms: -1 + 1 = 0
0 + p = 1.190238071 + 1
p = 1.190238071 + 1

Combine like terms: 1.190238071 + 1 = 2.190238071
p = 2.190238071

Simplifying
p = 2.190238071

Subproblem 2
p + -1 = -1.190238071

Simplifying
p + -1 = -1.190238071

Reorder the terms:
-1 + p = -1.190238071

Solving
-1 + p = -1.190238071

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -1.190238071 + 1

Combine like terms: -1 + 1 = 0
0 + p = -1.190238071 + 1
p = -1.190238071 + 1

Combine like terms: -1.190238071 + 1 = -0.190238071
p = -0.190238071

Simplifying
p = -0.190238071

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.190238071, -0.190238071}
Solution
p = {2.190238071, -0.190238071}