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

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

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

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

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

Combine like terms: 7 + -2 = 5
-1 + 3p = 5(-1 + p) * 2(5 + -1p)

Reorder the terms for easier multiplication:
-1 + 3p = 5 * 2(-1 + p)(5 + -1p)

Multiply 5 * 2
-1 + 3p = 10(-1 + p)(5 + -1p)

Multiply (-1 + p) * (5 + -1p)
-1 + 3p = 10(-1(5 + -1p) + p(5 + -1p))
-1 + 3p = 10((5 * -1 + -1p * -1) + p(5 + -1p))
-1 + 3p = 10((-5 + 1p) + p(5 + -1p))
-1 + 3p = 10(-5 + 1p + (5 * p + -1p * p))
-1 + 3p = 10(-5 + 1p + (5p + -1p2))

Combine like terms: 1p + 5p = 6p
-1 + 3p = 10(-5 + 6p + -1p2)
-1 + 3p = (-5 * 10 + 6p * 10 + -1p2 * 10)
-1 + 3p = (-50 + 60p + -10p2)

Solving
-1 + 3p = -50 + 60p + -10p2

Solving for variable 'p'.

Reorder the terms:
-1 + 50 + 3p + -60p + 10p2 = -50 + 60p + -10p2 + 50 + -60p + 10p2

Combine like terms: -1 + 50 = 49
49 + 3p + -60p + 10p2 = -50 + 60p + -10p2 + 50 + -60p + 10p2

Combine like terms: 3p + -60p = -57p
49 + -57p + 10p2 = -50 + 60p + -10p2 + 50 + -60p + 10p2

Reorder the terms:
49 + -57p + 10p2 = -50 + 50 + 60p + -60p + -10p2 + 10p2

Combine like terms: -50 + 50 = 0
49 + -57p + 10p2 = 0 + 60p + -60p + -10p2 + 10p2
49 + -57p + 10p2 = 60p + -60p + -10p2 + 10p2

Combine like terms: 60p + -60p = 0
49 + -57p + 10p2 = 0 + -10p2 + 10p2
49 + -57p + 10p2 = -10p2 + 10p2

Combine like terms: -10p2 + 10p2 = 0
49 + -57p + 10p2 = 0

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

Divide each side by '10'.
4.9 + -5.7p + p2 = 0

Move the constant term to the right:

Add '-4.9' to each side of the equation.
4.9 + -5.7p + -4.9 + p2 = 0 + -4.9

Reorder the terms:
4.9 + -4.9 + -5.7p + p2 = 0 + -4.9

Combine like terms: 4.9 + -4.9 = 0.0
0.0 + -5.7p + p2 = 0 + -4.9
-5.7p + p2 = 0 + -4.9

Combine like terms: 0 + -4.9 = -4.9
-5.7p + p2 = -4.9

The p term is -5.7p.  Take half its coefficient (-2.85).
Square it (8.1225) and add it to both sides.

Add '8.1225' to each side of the equation.
-5.7p + 8.1225 + p2 = -4.9 + 8.1225

Reorder the terms:
8.1225 + -5.7p + p2 = -4.9 + 8.1225

Combine like terms: -4.9 + 8.1225 = 3.2225
8.1225 + -5.7p + p2 = 3.2225

Factor a perfect square on the left side:
(p + -2.85)(p + -2.85) = 3.2225

Calculate the square root of the right side: 1.795132307

Break this problem into two subproblems by setting 
(p + -2.85) equal to 1.795132307 and -1.795132307.

Subproblem 1
p + -2.85 = 1.795132307

Simplifying
p + -2.85 = 1.795132307

Reorder the terms:
-2.85 + p = 1.795132307

Solving
-2.85 + p = 1.795132307

Solving for variable 'p'.

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

Add '2.85' to each side of the equation.
-2.85 + 2.85 + p = 1.795132307 + 2.85

Combine like terms: -2.85 + 2.85 = 0.00
0.00 + p = 1.795132307 + 2.85
p = 1.795132307 + 2.85

Combine like terms: 1.795132307 + 2.85 = 4.645132307
p = 4.645132307

Simplifying
p = 4.645132307

Subproblem 2
p + -2.85 = -1.795132307

Simplifying
p + -2.85 = -1.795132307

Reorder the terms:
-2.85 + p = -1.795132307

Solving
-2.85 + p = -1.795132307

Solving for variable 'p'.

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

Add '2.85' to each side of the equation.
-2.85 + 2.85 + p = -1.795132307 + 2.85

Combine like terms: -2.85 + 2.85 = 0.00
0.00 + p = -1.795132307 + 2.85
p = -1.795132307 + 2.85

Combine like terms: -1.795132307 + 2.85 = 1.054867693
p = 1.054867693

Simplifying
p = 1.054867693

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.645132307, 1.054867693}