6p^2-15p+1=0

Solution for 6p^2-15p+1=0 equation:

Simplifying
6p2 + -15p + 1 = 0

Reorder the terms:
1 + -15p + 6p2 = 0

Solving
1 + -15p + 6p2 = 0

Solving for variable 'p'.

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

Divide each side by '6'.
0.1666666667 + -2.5p + p2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -2.5p + -0.1666666667 + p2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -2.5p + p2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -2.5p + p2 = 0 + -0.1666666667
-2.5p + p2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-2.5p + p2 = -0.1666666667

The p term is -2.5p.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5p + 1.5625 + p2 = -0.1666666667 + 1.5625

Reorder the terms:
1.5625 + -2.5p + p2 = -0.1666666667 + 1.5625

Combine like terms: -0.1666666667 + 1.5625 = 1.3958333333
1.5625 + -2.5p + p2 = 1.3958333333

Factor a perfect square on the left side:
(p + -1.25)(p + -1.25) = 1.3958333333

Calculate the square root of the right side: 1.181453907

Break this problem into two subproblems by setting 
(p + -1.25) equal to 1.181453907 and -1.181453907.

Subproblem 1
p + -1.25 = 1.181453907

Simplifying
p + -1.25 = 1.181453907

Reorder the terms:
-1.25 + p = 1.181453907

Solving
-1.25 + p = 1.181453907

Solving for variable 'p'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + p = 1.181453907 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + p = 1.181453907 + 1.25
p = 1.181453907 + 1.25

Combine like terms: 1.181453907 + 1.25 = 2.431453907
p = 2.431453907

Simplifying
p = 2.431453907

Subproblem 2
p + -1.25 = -1.181453907

Simplifying
p + -1.25 = -1.181453907

Reorder the terms:
-1.25 + p = -1.181453907

Solving
-1.25 + p = -1.181453907

Solving for variable 'p'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + p = -1.181453907 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + p = -1.181453907 + 1.25
p = -1.181453907 + 1.25

Combine like terms: -1.181453907 + 1.25 = 0.068546093
p = 0.068546093

Simplifying
p = 0.068546093

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.431453907, 0.068546093}