3(5p-1)-4(3p-7)p=4

Solution for 3(5p-1)-4(3p-7)p=4 equation:

Simplifying
3(5p + -1) + -4(3p + -7) * p = 4

Reorder the terms:
3(-1 + 5p) + -4(3p + -7) * p = 4
(-1 * 3 + 5p * 3) + -4(3p + -7) * p = 4
(-3 + 15p) + -4(3p + -7) * p = 4

Reorder the terms:
-3 + 15p + -4(-7 + 3p) * p = 4

Reorder the terms for easier multiplication:
-3 + 15p + -4p(-7 + 3p) = 4
-3 + 15p + (-7 * -4p + 3p * -4p) = 4
-3 + 15p + (28p + -12p2) = 4

Combine like terms: 15p + 28p = 43p
-3 + 43p + -12p2 = 4

Solving
-3 + 43p + -12p2 = 4

Solving for variable 'p'.

Reorder the terms:
-3 + -4 + 43p + -12p2 = 4 + -4

Combine like terms: -3 + -4 = -7
-7 + 43p + -12p2 = 4 + -4

Combine like terms: 4 + -4 = 0
-7 + 43p + -12p2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
0.5833333333 + -3.583333333p + p2 = 0

Move the constant term to the right:

Add '-0.5833333333' to each side of the equation.
0.5833333333 + -3.583333333p + -0.5833333333 + p2 = 0 + -0.5833333333

Reorder the terms:
0.5833333333 + -0.5833333333 + -3.583333333p + p2 = 0 + -0.5833333333

Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000
0.0000000000 + -3.583333333p + p2 = 0 + -0.5833333333
-3.583333333p + p2 = 0 + -0.5833333333

Combine like terms: 0 + -0.5833333333 = -0.5833333333
-3.583333333p + p2 = -0.5833333333

The p term is -3.583333333p.  Take half its coefficient (-1.791666667).
Square it (3.210069446) and add it to both sides.

Add '3.210069446' to each side of the equation.
-3.583333333p + 3.210069446 + p2 = -0.5833333333 + 3.210069446

Reorder the terms:
3.210069446 + -3.583333333p + p2 = -0.5833333333 + 3.210069446

Combine like terms: -0.5833333333 + 3.210069446 = 2.6267361127
3.210069446 + -3.583333333p + p2 = 2.6267361127

Factor a perfect square on the left side:
(p + -1.791666667)(p + -1.791666667) = 2.6267361127

Calculate the square root of the right side: 1.620720862

Break this problem into two subproblems by setting 
(p + -1.791666667) equal to 1.620720862 and -1.620720862.

Subproblem 1
p + -1.791666667 = 1.620720862

Simplifying
p + -1.791666667 = 1.620720862

Reorder the terms:
-1.791666667 + p = 1.620720862

Solving
-1.791666667 + p = 1.620720862

Solving for variable 'p'.

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

Add '1.791666667' to each side of the equation.
-1.791666667 + 1.791666667 + p = 1.620720862 + 1.791666667

Combine like terms: -1.791666667 + 1.791666667 = 0.000000000
0.000000000 + p = 1.620720862 + 1.791666667
p = 1.620720862 + 1.791666667

Combine like terms: 1.620720862 + 1.791666667 = 3.412387529
p = 3.412387529

Simplifying
p = 3.412387529

Subproblem 2
p + -1.791666667 = -1.620720862

Simplifying
p + -1.791666667 = -1.620720862

Reorder the terms:
-1.791666667 + p = -1.620720862

Solving
-1.791666667 + p = -1.620720862

Solving for variable 'p'.

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

Add '1.791666667' to each side of the equation.
-1.791666667 + 1.791666667 + p = -1.620720862 + 1.791666667

Combine like terms: -1.791666667 + 1.791666667 = 0.000000000
0.000000000 + p = -1.620720862 + 1.791666667
p = -1.620720862 + 1.791666667

Combine like terms: -1.620720862 + 1.791666667 = 0.170945805
p = 0.170945805

Simplifying
p = 0.170945805

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.412387529, 0.170945805}