9p(3p-4)=15(6-p)

Solution for 9p(3p-4)=15(6-p) equation:

Simplifying
9p(3p + -4) = 15(6 + -1p)

Reorder the terms:
9p(-4 + 3p) = 15(6 + -1p)
(-4 * 9p + 3p * 9p) = 15(6 + -1p)
(-36p + 27p2) = 15(6 + -1p)
-36p + 27p2 = (6 * 15 + -1p * 15)
-36p + 27p2 = (90 + -15p)

Solving
-36p + 27p2 = 90 + -15p

Solving for variable 'p'.

Reorder the terms:
-90 + -36p + 15p + 27p2 = 90 + -15p + -90 + 15p

Combine like terms: -36p + 15p = -21p
-90 + -21p + 27p2 = 90 + -15p + -90 + 15p

Reorder the terms:
-90 + -21p + 27p2 = 90 + -90 + -15p + 15p

Combine like terms: 90 + -90 = 0
-90 + -21p + 27p2 = 0 + -15p + 15p
-90 + -21p + 27p2 = -15p + 15p

Combine like terms: -15p + 15p = 0
-90 + -21p + 27p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + -7p + 9p2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-30 + -7p + 9p2)' equal to zero and attempt to solve:

Simplifying
-30 + -7p + 9p2 = 0

Solving
-30 + -7p + 9p2 = 0

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

Divide each side by '9'.
-3.333333333 + -0.7777777778p + p2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -0.7777777778p + 3.333333333 + p2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -0.7777777778p + p2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -0.7777777778p + p2 = 0 + 3.333333333
-0.7777777778p + p2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-0.7777777778p + p2 = 3.333333333

The p term is -0.7777777778p.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778p + 0.1512345679 + p2 = 3.333333333 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778p + p2 = 3.333333333 + 0.1512345679

Combine like terms: 3.333333333 + 0.1512345679 = 3.4845679009
0.1512345679 + -0.7777777778p + p2 = 3.4845679009

Factor a perfect square on the left side:
(p + -0.3888888889)(p + -0.3888888889) = 3.4845679009

Calculate the square root of the right side: 1.866699735

Break this problem into two subproblems by setting 
(p + -0.3888888889) equal to 1.866699735 and -1.866699735.

Subproblem 1
p + -0.3888888889 = 1.866699735

Simplifying
p + -0.3888888889 = 1.866699735

Reorder the terms:
-0.3888888889 + p = 1.866699735

Solving
-0.3888888889 + p = 1.866699735

Solving for variable 'p'.

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

Add '0.3888888889' to each side of the equation.
-0.3888888889 + 0.3888888889 + p = 1.866699735 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + p = 1.866699735 + 0.3888888889
p = 1.866699735 + 0.3888888889

Combine like terms: 1.866699735 + 0.3888888889 = 2.2555886239
p = 2.2555886239

Simplifying
p = 2.2555886239

Subproblem 2
p + -0.3888888889 = -1.866699735

Simplifying
p + -0.3888888889 = -1.866699735

Reorder the terms:
-0.3888888889 + p = -1.866699735

Solving
-0.3888888889 + p = -1.866699735

Solving for variable 'p'.

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

Add '0.3888888889' to each side of the equation.
-0.3888888889 + 0.3888888889 + p = -1.866699735 + 0.3888888889

Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000
0.0000000000 + p = -1.866699735 + 0.3888888889
p = -1.866699735 + 0.3888888889

Combine like terms: -1.866699735 + 0.3888888889 = -1.4778108461
p = -1.4778108461

Simplifying
p = -1.4778108461

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.2555886239, -1.4778108461}
Solution
p = {2.2555886239, -1.4778108461}