4(p-6)p=6

Solution for 4(p-6)p=6 equation:

Simplifying
4(p + -6) * p = 6

Reorder the terms:
4(-6 + p) * p = 6

Reorder the terms for easier multiplication:
4p(-6 + p) = 6
(-6 * 4p + p * 4p) = 6
(-24p + 4p2) = 6

Solving
-24p + 4p2 = 6

Solving for variable 'p'.

Reorder the terms:
-6 + -24p + 4p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -24p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -12p + 2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -12p + 2p2)' equal to zero and attempt to solve:

Simplifying
-3 + -12p + 2p2 = 0

Solving
-3 + -12p + 2p2 = 0

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

Divide each side by '2'.
-1.5 + -6p + p2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -6p + 1.5 + p2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -6p + p2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -6p + p2 = 0 + 1.5
-6p + p2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-6p + p2 = 1.5

The p term is -6p.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6p + 9 + p2 = 1.5 + 9

Reorder the terms:
9 + -6p + p2 = 1.5 + 9

Combine like terms: 1.5 + 9 = 10.5
9 + -6p + p2 = 10.5

Factor a perfect square on the left side:
(p + -3)(p + -3) = 10.5

Calculate the square root of the right side: 3.240370349

Break this problem into two subproblems by setting 
(p + -3) equal to 3.240370349 and -3.240370349.

Subproblem 1
p + -3 = 3.240370349

Simplifying
p + -3 = 3.240370349

Reorder the terms:
-3 + p = 3.240370349

Solving
-3 + p = 3.240370349

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + p = 3.240370349 + 3

Combine like terms: -3 + 3 = 0
0 + p = 3.240370349 + 3
p = 3.240370349 + 3

Combine like terms: 3.240370349 + 3 = 6.240370349
p = 6.240370349

Simplifying
p = 6.240370349

Subproblem 2
p + -3 = -3.240370349

Simplifying
p + -3 = -3.240370349

Reorder the terms:
-3 + p = -3.240370349

Solving
-3 + p = -3.240370349

Solving for variable 'p'.

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

Add '3' to each side of the equation.
-3 + 3 + p = -3.240370349 + 3

Combine like terms: -3 + 3 = 0
0 + p = -3.240370349 + 3
p = -3.240370349 + 3

Combine like terms: -3.240370349 + 3 = -0.240370349
p = -0.240370349

Simplifying
p = -0.240370349

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.240370349, -0.240370349}
Solution
p = {6.240370349, -0.240370349}