4(3p^2+2p)-12p=2(8p+6)

Solution for 4(3p^2+2p)-12p=2(8p+6) equation:

Simplifying
4(3p2 + 2p) + -12p = 2(8p + 6)

Reorder the terms:
4(2p + 3p2) + -12p = 2(8p + 6)
(2p * 4 + 3p2 * 4) + -12p = 2(8p + 6)
(8p + 12p2) + -12p = 2(8p + 6)

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

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

Reorder the terms:
-4p + 12p2 = 2(6 + 8p)
-4p + 12p2 = (6 * 2 + 8p * 2)
-4p + 12p2 = (12 + 16p)

Solving
-4p + 12p2 = 12 + 16p

Solving for variable 'p'.

Reorder the terms:
-12 + -4p + -16p + 12p2 = 12 + 16p + -12 + -16p

Combine like terms: -4p + -16p = -20p
-12 + -20p + 12p2 = 12 + 16p + -12 + -16p

Reorder the terms:
-12 + -20p + 12p2 = 12 + -12 + 16p + -16p

Combine like terms: 12 + -12 = 0
-12 + -20p + 12p2 = 0 + 16p + -16p
-12 + -20p + 12p2 = 16p + -16p

Combine like terms: 16p + -16p = 0
-12 + -20p + 12p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -5p + 3p2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -5p + 3p2)' equal to zero and attempt to solve:

Simplifying
-3 + -5p + 3p2 = 0

Solving
-3 + -5p + 3p2 = 0

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

Divide each side by '3'.
-1 + -1.666666667p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.666666667p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.666666667p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.666666667p + p2 = 0 + 1
-1.666666667p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.666666667p + p2 = 1

The p term is -1.666666667p.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667p + 0.6944444447 + p2 = 1 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667p + p2 = 1 + 0.6944444447

Combine like terms: 1 + 0.6944444447 = 1.6944444447
0.6944444447 + -1.666666667p + p2 = 1.6944444447

Factor a perfect square on the left side:
(p + -0.8333333335)(p + -0.8333333335) = 1.6944444447

Calculate the square root of the right side: 1.301708279

Break this problem into two subproblems by setting 
(p + -0.8333333335) equal to 1.301708279 and -1.301708279.

Subproblem 1
p + -0.8333333335 = 1.301708279

Simplifying
p + -0.8333333335 = 1.301708279

Reorder the terms:
-0.8333333335 + p = 1.301708279

Solving
-0.8333333335 + p = 1.301708279

Solving for variable 'p'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + p = 1.301708279 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + p = 1.301708279 + 0.8333333335
p = 1.301708279 + 0.8333333335

Combine like terms: 1.301708279 + 0.8333333335 = 2.1350416125
p = 2.1350416125

Simplifying
p = 2.1350416125

Subproblem 2
p + -0.8333333335 = -1.301708279

Simplifying
p + -0.8333333335 = -1.301708279

Reorder the terms:
-0.8333333335 + p = -1.301708279

Solving
-0.8333333335 + p = -1.301708279

Solving for variable 'p'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + p = -1.301708279 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + p = -1.301708279 + 0.8333333335
p = -1.301708279 + 0.8333333335

Combine like terms: -1.301708279 + 0.8333333335 = -0.4683749455
p = -0.4683749455

Simplifying
p = -0.4683749455

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.1350416125, -0.4683749455}
Solution
p = {2.1350416125, -0.4683749455}