(3p-2)=(p-5)(9p+4)

Solution for (3p-2)=(p-5)(9p+4) equation:

Simplifying
(3p + -2) = (p + -5)(9p + 4)

Reorder the terms:
(-2 + 3p) = (p + -5)(9p + 4)

Remove parenthesis around (-2 + 3p)
-2 + 3p = (p + -5)(9p + 4)

Reorder the terms:
-2 + 3p = (-5 + p)(9p + 4)

Reorder the terms:
-2 + 3p = (-5 + p)(4 + 9p)

Multiply (-5 + p) * (4 + 9p)
-2 + 3p = (-5(4 + 9p) + p(4 + 9p))
-2 + 3p = ((4 * -5 + 9p * -5) + p(4 + 9p))
-2 + 3p = ((-20 + -45p) + p(4 + 9p))
-2 + 3p = (-20 + -45p + (4 * p + 9p * p))
-2 + 3p = (-20 + -45p + (4p + 9p2))

Combine like terms: -45p + 4p = -41p
-2 + 3p = (-20 + -41p + 9p2)

Solving
-2 + 3p = -20 + -41p + 9p2

Solving for variable 'p'.

Reorder the terms:
-2 + 20 + 3p + 41p + -9p2 = -20 + -41p + 9p2 + 20 + 41p + -9p2

Combine like terms: -2 + 20 = 18
18 + 3p + 41p + -9p2 = -20 + -41p + 9p2 + 20 + 41p + -9p2

Combine like terms: 3p + 41p = 44p
18 + 44p + -9p2 = -20 + -41p + 9p2 + 20 + 41p + -9p2

Reorder the terms:
18 + 44p + -9p2 = -20 + 20 + -41p + 41p + 9p2 + -9p2

Combine like terms: -20 + 20 = 0
18 + 44p + -9p2 = 0 + -41p + 41p + 9p2 + -9p2
18 + 44p + -9p2 = -41p + 41p + 9p2 + -9p2

Combine like terms: -41p + 41p = 0
18 + 44p + -9p2 = 0 + 9p2 + -9p2
18 + 44p + -9p2 = 9p2 + -9p2

Combine like terms: 9p2 + -9p2 = 0
18 + 44p + -9p2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-2 + -4.888888889p + p2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4.888888889p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + -4.888888889p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4.888888889p + p2 = 0 + 2
-4.888888889p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4.888888889p + p2 = 2

The p term is -4.888888889p.  Take half its coefficient (-2.444444445).
Square it (5.975308645) and add it to both sides.

Add '5.975308645' to each side of the equation.
-4.888888889p + 5.975308645 + p2 = 2 + 5.975308645

Reorder the terms:
5.975308645 + -4.888888889p + p2 = 2 + 5.975308645

Combine like terms: 2 + 5.975308645 = 7.975308645
5.975308645 + -4.888888889p + p2 = 7.975308645

Factor a perfect square on the left side:
(p + -2.444444445)(p + -2.444444445) = 7.975308645

Calculate the square root of the right side: 2.824058895

Break this problem into two subproblems by setting 
(p + -2.444444445) equal to 2.824058895 and -2.824058895.

Subproblem 1
p + -2.444444445 = 2.824058895

Simplifying
p + -2.444444445 = 2.824058895

Reorder the terms:
-2.444444445 + p = 2.824058895

Solving
-2.444444445 + p = 2.824058895

Solving for variable 'p'.

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

Add '2.444444445' to each side of the equation.
-2.444444445 + 2.444444445 + p = 2.824058895 + 2.444444445

Combine like terms: -2.444444445 + 2.444444445 = 0.000000000
0.000000000 + p = 2.824058895 + 2.444444445
p = 2.824058895 + 2.444444445

Combine like terms: 2.824058895 + 2.444444445 = 5.26850334
p = 5.26850334

Simplifying
p = 5.26850334

Subproblem 2
p + -2.444444445 = -2.824058895

Simplifying
p + -2.444444445 = -2.824058895

Reorder the terms:
-2.444444445 + p = -2.824058895

Solving
-2.444444445 + p = -2.824058895

Solving for variable 'p'.

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

Add '2.444444445' to each side of the equation.
-2.444444445 + 2.444444445 + p = -2.824058895 + 2.444444445

Combine like terms: -2.444444445 + 2.444444445 = 0.000000000
0.000000000 + p = -2.824058895 + 2.444444445
p = -2.824058895 + 2.444444445

Combine like terms: -2.824058895 + 2.444444445 = -0.37961445
p = -0.37961445

Simplifying
p = -0.37961445

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.26850334, -0.37961445}