3p-1=5p(p-1)-2(7-2p)

Solution for 3p-1=5p(p-1)-2(7-2p) equation:

Simplifying
3p + -1 = 5p(p + -1) + -2(7 + -2p)

Reorder the terms:
-1 + 3p = 5p(p + -1) + -2(7 + -2p)

Reorder the terms:
-1 + 3p = 5p(-1 + p) + -2(7 + -2p)
-1 + 3p = (-1 * 5p + p * 5p) + -2(7 + -2p)
-1 + 3p = (-5p + 5p2) + -2(7 + -2p)
-1 + 3p = -5p + 5p2 + (7 * -2 + -2p * -2)
-1 + 3p = -5p + 5p2 + (-14 + 4p)

Reorder the terms:
-1 + 3p = -14 + -5p + 4p + 5p2

Combine like terms: -5p + 4p = -1p
-1 + 3p = -14 + -1p + 5p2

Solving
-1 + 3p = -14 + -1p + 5p2

Solving for variable 'p'.

Reorder the terms:
-1 + 14 + 3p + p + -5p2 = -14 + -1p + 5p2 + 14 + p + -5p2

Combine like terms: -1 + 14 = 13
13 + 3p + p + -5p2 = -14 + -1p + 5p2 + 14 + p + -5p2

Combine like terms: 3p + p = 4p
13 + 4p + -5p2 = -14 + -1p + 5p2 + 14 + p + -5p2

Reorder the terms:
13 + 4p + -5p2 = -14 + 14 + -1p + p + 5p2 + -5p2

Combine like terms: -14 + 14 = 0
13 + 4p + -5p2 = 0 + -1p + p + 5p2 + -5p2
13 + 4p + -5p2 = -1p + p + 5p2 + -5p2

Combine like terms: -1p + p = 0
13 + 4p + -5p2 = 0 + 5p2 + -5p2
13 + 4p + -5p2 = 5p2 + -5p2

Combine like terms: 5p2 + -5p2 = 0
13 + 4p + -5p2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-2.6 + -0.8p + p2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + -0.8p + 2.6 + p2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + -0.8p + p2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + -0.8p + p2 = 0 + 2.6
-0.8p + p2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
-0.8p + p2 = 2.6

The p term is -0.8p.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8p + 0.16 + p2 = 2.6 + 0.16

Reorder the terms:
0.16 + -0.8p + p2 = 2.6 + 0.16

Combine like terms: 2.6 + 0.16 = 2.76
0.16 + -0.8p + p2 = 2.76

Factor a perfect square on the left side:
(p + -0.4)(p + -0.4) = 2.76

Calculate the square root of the right side: 1.661324773

Break this problem into two subproblems by setting 
(p + -0.4) equal to 1.661324773 and -1.661324773.

Subproblem 1
p + -0.4 = 1.661324773

Simplifying
p + -0.4 = 1.661324773

Reorder the terms:
-0.4 + p = 1.661324773

Solving
-0.4 + p = 1.661324773

Solving for variable 'p'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + p = 1.661324773 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + p = 1.661324773 + 0.4
p = 1.661324773 + 0.4

Combine like terms: 1.661324773 + 0.4 = 2.061324773
p = 2.061324773

Simplifying
p = 2.061324773

Subproblem 2
p + -0.4 = -1.661324773

Simplifying
p + -0.4 = -1.661324773

Reorder the terms:
-0.4 + p = -1.661324773

Solving
-0.4 + p = -1.661324773

Solving for variable 'p'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + p = -1.661324773 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + p = -1.661324773 + 0.4
p = -1.661324773 + 0.4

Combine like terms: -1.661324773 + 0.4 = -1.261324773
p = -1.261324773

Simplifying
p = -1.261324773

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.061324773, -1.261324773}