-3p-3(4-3p)=2p(p-4)-4

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

Simplifying
-3p + -3(4 + -3p) = 2p(p + -4) + -4
-3p + (4 * -3 + -3p * -3) = 2p(p + -4) + -4
-3p + (-12 + 9p) = 2p(p + -4) + -4

Reorder the terms:
-12 + -3p + 9p = 2p(p + -4) + -4

Combine like terms: -3p + 9p = 6p
-12 + 6p = 2p(p + -4) + -4

Reorder the terms:
-12 + 6p = 2p(-4 + p) + -4
-12 + 6p = (-4 * 2p + p * 2p) + -4
-12 + 6p = (-8p + 2p2) + -4

Reorder the terms:
-12 + 6p = -4 + -8p + 2p2

Solving
-12 + 6p = -4 + -8p + 2p2

Solving for variable 'p'.

Reorder the terms:
-12 + 4 + 6p + 8p + -2p2 = -4 + -8p + 2p2 + 4 + 8p + -2p2

Combine like terms: -12 + 4 = -8
-8 + 6p + 8p + -2p2 = -4 + -8p + 2p2 + 4 + 8p + -2p2

Combine like terms: 6p + 8p = 14p
-8 + 14p + -2p2 = -4 + -8p + 2p2 + 4 + 8p + -2p2

Reorder the terms:
-8 + 14p + -2p2 = -4 + 4 + -8p + 8p + 2p2 + -2p2

Combine like terms: -4 + 4 = 0
-8 + 14p + -2p2 = 0 + -8p + 8p + 2p2 + -2p2
-8 + 14p + -2p2 = -8p + 8p + 2p2 + -2p2

Combine like terms: -8p + 8p = 0
-8 + 14p + -2p2 = 0 + 2p2 + -2p2
-8 + 14p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-8 + 14p + -2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 7p + -1p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 7p + -1p2)' equal to zero and attempt to solve:

Simplifying
-4 + 7p + -1p2 = 0

Solving
-4 + 7p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -7p + p2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -7p + -4 + p2 = 0 + -4

Reorder the terms:
4 + -4 + -7p + p2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7p + p2 = 0 + -4
-7p + p2 = 0 + -4

Combine like terms: 0 + -4 = -4
-7p + p2 = -4

The p term is -7p.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7p + 12.25 + p2 = -4 + 12.25

Reorder the terms:
12.25 + -7p + p2 = -4 + 12.25

Combine like terms: -4 + 12.25 = 8.25
12.25 + -7p + p2 = 8.25

Factor a perfect square on the left side:
(p + -3.5)(p + -3.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(p + -3.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
p + -3.5 = 2.872281323

Simplifying
p + -3.5 = 2.872281323

Reorder the terms:
-3.5 + p = 2.872281323

Solving
-3.5 + p = 2.872281323

Solving for variable 'p'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + p = 2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p = 2.872281323 + 3.5
p = 2.872281323 + 3.5

Combine like terms: 2.872281323 + 3.5 = 6.372281323
p = 6.372281323

Simplifying
p = 6.372281323

Subproblem 2
p + -3.5 = -2.872281323

Simplifying
p + -3.5 = -2.872281323

Reorder the terms:
-3.5 + p = -2.872281323

Solving
-3.5 + p = -2.872281323

Solving for variable 'p'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + p = -2.872281323 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p = -2.872281323 + 3.5
p = -2.872281323 + 3.5

Combine like terms: -2.872281323 + 3.5 = 0.627718677
p = 0.627718677

Simplifying
p = 0.627718677

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.372281323, 0.627718677}
Solution
p = {6.372281323, 0.627718677}