6p(1.3p-3)=2.6p-5

Solution for 6p(1.3p-3)=2.6p-5 equation:

Simplifying
6p(1.3p + -3) = 2.6p + -5

Reorder the terms:
6p(-3 + 1.3p) = 2.6p + -5
(-3 * 6p + 1.3p * 6p) = 2.6p + -5
(-18p + 7.8p2) = 2.6p + -5

Reorder the terms:
-18p + 7.8p2 = -5 + 2.6p

Solving
-18p + 7.8p2 = -5 + 2.6p

Solving for variable 'p'.

Reorder the terms:
5 + -18p + -2.6p + 7.8p2 = -5 + 2.6p + 5 + -2.6p

Combine like terms: -18p + -2.6p = -20.6p
5 + -20.6p + 7.8p2 = -5 + 2.6p + 5 + -2.6p

Reorder the terms:
5 + -20.6p + 7.8p2 = -5 + 5 + 2.6p + -2.6p

Combine like terms: -5 + 5 = 0
5 + -20.6p + 7.8p2 = 0 + 2.6p + -2.6p
5 + -20.6p + 7.8p2 = 2.6p + -2.6p

Combine like terms: 2.6p + -2.6p = 0.0
5 + -20.6p + 7.8p2 = 0.0

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

Divide each side by '7.8'.
0.641025641 + -2.641025641p + p2 = 0

Move the constant term to the right:

Add '-0.641025641' to each side of the equation.
0.641025641 + -2.641025641p + -0.641025641 + p2 = 0 + -0.641025641

Reorder the terms:
0.641025641 + -0.641025641 + -2.641025641p + p2 = 0 + -0.641025641

Combine like terms: 0.641025641 + -0.641025641 = 0.000000000
0.000000000 + -2.641025641p + p2 = 0 + -0.641025641
-2.641025641p + p2 = 0 + -0.641025641

Combine like terms: 0 + -0.641025641 = -0.641025641
-2.641025641p + p2 = -0.641025641

The p term is -2.641025641p.  Take half its coefficient (-1.320512821).
Square it (1.743754110) and add it to both sides.

Add '1.743754110' to each side of the equation.
-2.641025641p + 1.743754110 + p2 = -0.641025641 + 1.743754110

Reorder the terms:
1.743754110 + -2.641025641p + p2 = -0.641025641 + 1.743754110

Combine like terms: -0.641025641 + 1.743754110 = 1.102728469
1.743754110 + -2.641025641p + p2 = 1.102728469

Factor a perfect square on the left side:
(p + -1.320512821)(p + -1.320512821) = 1.102728469

Calculate the square root of the right side: 1.050108789

Break this problem into two subproblems by setting 
(p + -1.320512821) equal to 1.050108789 and -1.050108789.

Subproblem 1
p + -1.320512821 = 1.050108789

Simplifying
p + -1.320512821 = 1.050108789

Reorder the terms:
-1.320512821 + p = 1.050108789

Solving
-1.320512821 + p = 1.050108789

Solving for variable 'p'.

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

Add '1.320512821' to each side of the equation.
-1.320512821 + 1.320512821 + p = 1.050108789 + 1.320512821

Combine like terms: -1.320512821 + 1.320512821 = 0.000000000
0.000000000 + p = 1.050108789 + 1.320512821
p = 1.050108789 + 1.320512821

Combine like terms: 1.050108789 + 1.320512821 = 2.37062161
p = 2.37062161

Simplifying
p = 2.37062161

Subproblem 2
p + -1.320512821 = -1.050108789

Simplifying
p + -1.320512821 = -1.050108789

Reorder the terms:
-1.320512821 + p = -1.050108789

Solving
-1.320512821 + p = -1.050108789

Solving for variable 'p'.

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

Add '1.320512821' to each side of the equation.
-1.320512821 + 1.320512821 + p = -1.050108789 + 1.320512821

Combine like terms: -1.320512821 + 1.320512821 = 0.000000000
0.000000000 + p = -1.050108789 + 1.320512821
p = -1.050108789 + 1.320512821

Combine like terms: -1.050108789 + 1.320512821 = 0.270404032
p = 0.270404032

Simplifying
p = 0.270404032

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.37062161, 0.270404032}