10p-2(3p-6)=4(3p-6)8p

Solution for 10p-2(3p-6)=4(3p-6)8p equation:

Simplifying
10p + -2(3p + -6) = 4(3p + -6) * 8p

Reorder the terms:
10p + -2(-6 + 3p) = 4(3p + -6) * 8p
10p + (-6 * -2 + 3p * -2) = 4(3p + -6) * 8p
10p + (12 + -6p) = 4(3p + -6) * 8p

Reorder the terms:
12 + 10p + -6p = 4(3p + -6) * 8p

Combine like terms: 10p + -6p = 4p
12 + 4p = 4(3p + -6) * 8p

Reorder the terms:
12 + 4p = 4(-6 + 3p) * 8p

Reorder the terms for easier multiplication:
12 + 4p = 4 * 8p(-6 + 3p)

Multiply 4 * 8
12 + 4p = 32p(-6 + 3p)
12 + 4p = (-6 * 32p + 3p * 32p)
12 + 4p = (-192p + 96p2)

Solving
12 + 4p = -192p + 96p2

Solving for variable 'p'.

Combine like terms: 4p + 192p = 196p
12 + 196p + -96p2 = -192p + 96p2 + 192p + -96p2

Reorder the terms:
12 + 196p + -96p2 = -192p + 192p + 96p2 + -96p2

Combine like terms: -192p + 192p = 0
12 + 196p + -96p2 = 0 + 96p2 + -96p2
12 + 196p + -96p2 = 96p2 + -96p2

Combine like terms: 96p2 + -96p2 = 0
12 + 196p + -96p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 49p + -24p2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + 49p + -24p2)' equal to zero and attempt to solve:

Simplifying
3 + 49p + -24p2 = 0

Solving
3 + 49p + -24p2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-0.125 + -2.041666667p + p2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -2.041666667p + 0.125 + p2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -2.041666667p + p2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -2.041666667p + p2 = 0 + 0.125
-2.041666667p + p2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-2.041666667p + p2 = 0.125

The p term is -2.041666667p.  Take half its coefficient (-1.020833334).
Square it (1.042100696) and add it to both sides.

Add '1.042100696' to each side of the equation.
-2.041666667p + 1.042100696 + p2 = 0.125 + 1.042100696

Reorder the terms:
1.042100696 + -2.041666667p + p2 = 0.125 + 1.042100696

Combine like terms: 0.125 + 1.042100696 = 1.167100696
1.042100696 + -2.041666667p + p2 = 1.167100696

Factor a perfect square on the left side:
(p + -1.020833334)(p + -1.020833334) = 1.167100696

Calculate the square root of the right side: 1.080324348

Break this problem into two subproblems by setting 
(p + -1.020833334) equal to 1.080324348 and -1.080324348.

Subproblem 1
p + -1.020833334 = 1.080324348

Simplifying
p + -1.020833334 = 1.080324348

Reorder the terms:
-1.020833334 + p = 1.080324348

Solving
-1.020833334 + p = 1.080324348

Solving for variable 'p'.

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

Add '1.020833334' to each side of the equation.
-1.020833334 + 1.020833334 + p = 1.080324348 + 1.020833334

Combine like terms: -1.020833334 + 1.020833334 = 0.000000000
0.000000000 + p = 1.080324348 + 1.020833334
p = 1.080324348 + 1.020833334

Combine like terms: 1.080324348 + 1.020833334 = 2.101157682
p = 2.101157682

Simplifying
p = 2.101157682

Subproblem 2
p + -1.020833334 = -1.080324348

Simplifying
p + -1.020833334 = -1.080324348

Reorder the terms:
-1.020833334 + p = -1.080324348

Solving
-1.020833334 + p = -1.080324348

Solving for variable 'p'.

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

Add '1.020833334' to each side of the equation.
-1.020833334 + 1.020833334 + p = -1.080324348 + 1.020833334

Combine like terms: -1.020833334 + 1.020833334 = 0.000000000
0.000000000 + p = -1.080324348 + 1.020833334
p = -1.080324348 + 1.020833334

Combine like terms: -1.080324348 + 1.020833334 = -0.059491014
p = -0.059491014

Simplifying
p = -0.059491014

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.101157682, -0.059491014}
Solution
p = {2.101157682, -0.059491014}