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

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

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

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

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

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

Multiply 5 * 2
-1 + 3p = 10(-1 + p)(7 + -2p)

Multiply (-1 + p) * (7 + -2p)
-1 + 3p = 10(-1(7 + -2p) + p(7 + -2p))
-1 + 3p = 10((7 * -1 + -2p * -1) + p(7 + -2p))
-1 + 3p = 10((-7 + 2p) + p(7 + -2p))
-1 + 3p = 10(-7 + 2p + (7 * p + -2p * p))
-1 + 3p = 10(-7 + 2p + (7p + -2p2))

Combine like terms: 2p + 7p = 9p
-1 + 3p = 10(-7 + 9p + -2p2)
-1 + 3p = (-7 * 10 + 9p * 10 + -2p2 * 10)
-1 + 3p = (-70 + 90p + -20p2)

Solving
-1 + 3p = -70 + 90p + -20p2

Solving for variable 'p'.

Reorder the terms:
-1 + 70 + 3p + -90p + 20p2 = -70 + 90p + -20p2 + 70 + -90p + 20p2

Combine like terms: -1 + 70 = 69
69 + 3p + -90p + 20p2 = -70 + 90p + -20p2 + 70 + -90p + 20p2

Combine like terms: 3p + -90p = -87p
69 + -87p + 20p2 = -70 + 90p + -20p2 + 70 + -90p + 20p2

Reorder the terms:
69 + -87p + 20p2 = -70 + 70 + 90p + -90p + -20p2 + 20p2

Combine like terms: -70 + 70 = 0
69 + -87p + 20p2 = 0 + 90p + -90p + -20p2 + 20p2
69 + -87p + 20p2 = 90p + -90p + -20p2 + 20p2

Combine like terms: 90p + -90p = 0
69 + -87p + 20p2 = 0 + -20p2 + 20p2
69 + -87p + 20p2 = -20p2 + 20p2

Combine like terms: -20p2 + 20p2 = 0
69 + -87p + 20p2 = 0

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

Divide each side by '20'.
3.45 + -4.35p + p2 = 0

Move the constant term to the right:

Add '-3.45' to each side of the equation.
3.45 + -4.35p + -3.45 + p2 = 0 + -3.45

Reorder the terms:
3.45 + -3.45 + -4.35p + p2 = 0 + -3.45

Combine like terms: 3.45 + -3.45 = 0.00
0.00 + -4.35p + p2 = 0 + -3.45
-4.35p + p2 = 0 + -3.45

Combine like terms: 0 + -3.45 = -3.45
-4.35p + p2 = -3.45

The p term is -4.35p.  Take half its coefficient (-2.175).
Square it (4.730625) and add it to both sides.

Add '4.730625' to each side of the equation.
-4.35p + 4.730625 + p2 = -3.45 + 4.730625

Reorder the terms:
4.730625 + -4.35p + p2 = -3.45 + 4.730625

Combine like terms: -3.45 + 4.730625 = 1.280625
4.730625 + -4.35p + p2 = 1.280625

Factor a perfect square on the left side:
(p + -2.175)(p + -2.175) = 1.280625

Calculate the square root of the right side: 1.13164703

Break this problem into two subproblems by setting 
(p + -2.175) equal to 1.13164703 and -1.13164703.

Subproblem 1
p + -2.175 = 1.13164703

Simplifying
p + -2.175 = 1.13164703

Reorder the terms:
-2.175 + p = 1.13164703

Solving
-2.175 + p = 1.13164703

Solving for variable 'p'.

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

Add '2.175' to each side of the equation.
-2.175 + 2.175 + p = 1.13164703 + 2.175

Combine like terms: -2.175 + 2.175 = 0.000
0.000 + p = 1.13164703 + 2.175
p = 1.13164703 + 2.175

Combine like terms: 1.13164703 + 2.175 = 3.30664703
p = 3.30664703

Simplifying
p = 3.30664703

Subproblem 2
p + -2.175 = -1.13164703

Simplifying
p + -2.175 = -1.13164703

Reorder the terms:
-2.175 + p = -1.13164703

Solving
-2.175 + p = -1.13164703

Solving for variable 'p'.

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

Add '2.175' to each side of the equation.
-2.175 + 2.175 + p = -1.13164703 + 2.175

Combine like terms: -2.175 + 2.175 = 0.000
0.000 + p = -1.13164703 + 2.175
p = -1.13164703 + 2.175

Combine like terms: -1.13164703 + 2.175 = 1.04335297
p = 1.04335297

Simplifying
p = 1.04335297

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.30664703, 1.04335297}