6p(-5p+5)=-8-2(p+12)

Solution for 6p(-5p+5)=-8-2(p+12) equation:

Simplifying
6p(-5p + 5) = -8 + -2(p + 12)

Reorder the terms:
6p(5 + -5p) = -8 + -2(p + 12)
(5 * 6p + -5p * 6p) = -8 + -2(p + 12)
(30p + -30p2) = -8 + -2(p + 12)

Reorder the terms:
30p + -30p2 = -8 + -2(12 + p)
30p + -30p2 = -8 + (12 * -2 + p * -2)
30p + -30p2 = -8 + (-24 + -2p)

Combine like terms: -8 + -24 = -32
30p + -30p2 = -32 + -2p

Solving
30p + -30p2 = -32 + -2p

Solving for variable 'p'.

Reorder the terms:
32 + 30p + 2p + -30p2 = -32 + -2p + 32 + 2p

Combine like terms: 30p + 2p = 32p
32 + 32p + -30p2 = -32 + -2p + 32 + 2p

Reorder the terms:
32 + 32p + -30p2 = -32 + 32 + -2p + 2p

Combine like terms: -32 + 32 = 0
32 + 32p + -30p2 = 0 + -2p + 2p
32 + 32p + -30p2 = -2p + 2p

Combine like terms: -2p + 2p = 0
32 + 32p + -30p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 16p + -15p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(16 + 16p + -15p2)' equal to zero and attempt to solve:

Simplifying
16 + 16p + -15p2 = 0

Solving
16 + 16p + -15p2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-1.066666667 + -1.066666667p + p2 = 0

Move the constant term to the right:

Add '1.066666667' to each side of the equation.
-1.066666667 + -1.066666667p + 1.066666667 + p2 = 0 + 1.066666667

Reorder the terms:
-1.066666667 + 1.066666667 + -1.066666667p + p2 = 0 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + -1.066666667p + p2 = 0 + 1.066666667
-1.066666667p + p2 = 0 + 1.066666667

Combine like terms: 0 + 1.066666667 = 1.066666667
-1.066666667p + p2 = 1.066666667

The p term is -1.066666667p.  Take half its coefficient (-0.5333333335).
Square it (0.2844444446) and add it to both sides.

Add '0.2844444446' to each side of the equation.
-1.066666667p + 0.2844444446 + p2 = 1.066666667 + 0.2844444446

Reorder the terms:
0.2844444446 + -1.066666667p + p2 = 1.066666667 + 0.2844444446

Combine like terms: 1.066666667 + 0.2844444446 = 1.3511111116
0.2844444446 + -1.066666667p + p2 = 1.3511111116

Factor a perfect square on the left side:
(p + -0.5333333335)(p + -0.5333333335) = 1.3511111116

Calculate the square root of the right side: 1.162373052

Break this problem into two subproblems by setting 
(p + -0.5333333335) equal to 1.162373052 and -1.162373052.

Subproblem 1
p + -0.5333333335 = 1.162373052

Simplifying
p + -0.5333333335 = 1.162373052

Reorder the terms:
-0.5333333335 + p = 1.162373052

Solving
-0.5333333335 + p = 1.162373052

Solving for variable 'p'.

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

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + p = 1.162373052 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + p = 1.162373052 + 0.5333333335
p = 1.162373052 + 0.5333333335

Combine like terms: 1.162373052 + 0.5333333335 = 1.6957063855
p = 1.6957063855

Simplifying
p = 1.6957063855

Subproblem 2
p + -0.5333333335 = -1.162373052

Simplifying
p + -0.5333333335 = -1.162373052

Reorder the terms:
-0.5333333335 + p = -1.162373052

Solving
-0.5333333335 + p = -1.162373052

Solving for variable 'p'.

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

Add '0.5333333335' to each side of the equation.
-0.5333333335 + 0.5333333335 + p = -1.162373052 + 0.5333333335

Combine like terms: -0.5333333335 + 0.5333333335 = 0.0000000000
0.0000000000 + p = -1.162373052 + 0.5333333335
p = -1.162373052 + 0.5333333335

Combine like terms: -1.162373052 + 0.5333333335 = -0.6290397185
p = -0.6290397185

Simplifying
p = -0.6290397185

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.6957063855, -0.6290397185}
Solution
p = {1.6957063855, -0.6290397185}