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

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

Simplifying
-6p(-1p + 8) = -6p + 12

Reorder the terms:
-6p(8 + -1p) = -6p + 12
(8 * -6p + -1p * -6p) = -6p + 12
(-48p + 6p2) = -6p + 12

Reorder the terms:
-48p + 6p2 = 12 + -6p

Solving
-48p + 6p2 = 12 + -6p

Solving for variable 'p'.

Reorder the terms:
-12 + -48p + 6p + 6p2 = 12 + -6p + -12 + 6p

Combine like terms: -48p + 6p = -42p
-12 + -42p + 6p2 = 12 + -6p + -12 + 6p

Reorder the terms:
-12 + -42p + 6p2 = 12 + -12 + -6p + 6p

Combine like terms: 12 + -12 = 0
-12 + -42p + 6p2 = 0 + -6p + 6p
-12 + -42p + 6p2 = -6p + 6p

Combine like terms: -6p + 6p = 0
-12 + -42p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + -7p + p2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-2 + -7p + p2)' equal to zero and attempt to solve:

Simplifying
-2 + -7p + p2 = 0

Solving
-2 + -7p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -7p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + -7p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7p + p2 = 0 + 2
-7p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
-7p + p2 = 2

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 = 2 + 12.25

Reorder the terms:
12.25 + -7p + p2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + -7p + p2 = 14.25

Factor a perfect square on the left side:
(p + -3.5)(p + -3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(p + -3.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
p + -3.5 = 3.774917218

Simplifying
p + -3.5 = 3.774917218

Reorder the terms:
-3.5 + p = 3.774917218

Solving
-3.5 + p = 3.774917218

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 = 3.774917218 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p = 3.774917218 + 3.5
p = 3.774917218 + 3.5

Combine like terms: 3.774917218 + 3.5 = 7.274917218
p = 7.274917218

Simplifying
p = 7.274917218

Subproblem 2
p + -3.5 = -3.774917218

Simplifying
p + -3.5 = -3.774917218

Reorder the terms:
-3.5 + p = -3.774917218

Solving
-3.5 + p = -3.774917218

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 = -3.774917218 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + p = -3.774917218 + 3.5
p = -3.774917218 + 3.5

Combine like terms: -3.774917218 + 3.5 = -0.274917218
p = -0.274917218

Simplifying
p = -0.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {7.274917218, -0.274917218}
Solution
p = {7.274917218, -0.274917218}