-7p-12=-2p+3(-4-p)2p

Solution for -7p-12=-2p+3(-4-p)2p equation:

Simplifying
-7p + -12 = -2p + 3(-4 + -1p) * 2p

Reorder the terms:
-12 + -7p = -2p + 3(-4 + -1p) * 2p

Reorder the terms for easier multiplication:
-12 + -7p = -2p + 3 * 2p(-4 + -1p)

Multiply 3 * 2
-12 + -7p = -2p + 6p(-4 + -1p)
-12 + -7p = -2p + (-4 * 6p + -1p * 6p)
-12 + -7p = -2p + (-24p + -6p2)

Combine like terms: -2p + -24p = -26p
-12 + -7p = -26p + -6p2

Solving
-12 + -7p = -26p + -6p2

Solving for variable 'p'.

Combine like terms: -7p + 26p = 19p
-12 + 19p + 6p2 = -26p + -6p2 + 26p + 6p2

Reorder the terms:
-12 + 19p + 6p2 = -26p + 26p + -6p2 + 6p2

Combine like terms: -26p + 26p = 0
-12 + 19p + 6p2 = 0 + -6p2 + 6p2
-12 + 19p + 6p2 = -6p2 + 6p2

Combine like terms: -6p2 + 6p2 = 0
-12 + 19p + 6p2 = 0

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

Divide each side by '6'.
-2 + 3.166666667p + p2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3.166666667p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + 3.166666667p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3.166666667p + p2 = 0 + 2
3.166666667p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
3.166666667p + p2 = 2

The p term is 3.166666667p.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667p + 2.506944447 + p2 = 2 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667p + p2 = 2 + 2.506944447

Combine like terms: 2 + 2.506944447 = 4.506944447
2.506944447 + 3.166666667p + p2 = 4.506944447

Factor a perfect square on the left side:
(p + 1.583333334)(p + 1.583333334) = 4.506944447

Calculate the square root of the right side: 2.122956534

Break this problem into two subproblems by setting 
(p + 1.583333334) equal to 2.122956534 and -2.122956534.

Subproblem 1
p + 1.583333334 = 2.122956534

Simplifying
p + 1.583333334 = 2.122956534

Reorder the terms:
1.583333334 + p = 2.122956534

Solving
1.583333334 + p = 2.122956534

Solving for variable 'p'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + p = 2.122956534 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + p = 2.122956534 + -1.583333334
p = 2.122956534 + -1.583333334

Combine like terms: 2.122956534 + -1.583333334 = 0.5396232
p = 0.5396232

Simplifying
p = 0.5396232

Subproblem 2
p + 1.583333334 = -2.122956534

Simplifying
p + 1.583333334 = -2.122956534

Reorder the terms:
1.583333334 + p = -2.122956534

Solving
1.583333334 + p = -2.122956534

Solving for variable 'p'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + p = -2.122956534 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + p = -2.122956534 + -1.583333334
p = -2.122956534 + -1.583333334

Combine like terms: -2.122956534 + -1.583333334 = -3.706289868
p = -3.706289868

Simplifying
p = -3.706289868

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.5396232, -3.706289868}