2p(5p-6)=23(7-2p)

Solution for 2p(5p-6)=23(7-2p) equation:

Simplifying
2p(5p + -6) = 23(7 + -2p)

Reorder the terms:
2p(-6 + 5p) = 23(7 + -2p)
(-6 * 2p + 5p * 2p) = 23(7 + -2p)
(-12p + 10p2) = 23(7 + -2p)
-12p + 10p2 = (7 * 23 + -2p * 23)
-12p + 10p2 = (161 + -46p)

Solving
-12p + 10p2 = 161 + -46p

Solving for variable 'p'.

Reorder the terms:
-161 + -12p + 46p + 10p2 = 161 + -46p + -161 + 46p

Combine like terms: -12p + 46p = 34p
-161 + 34p + 10p2 = 161 + -46p + -161 + 46p

Reorder the terms:
-161 + 34p + 10p2 = 161 + -161 + -46p + 46p

Combine like terms: 161 + -161 = 0
-161 + 34p + 10p2 = 0 + -46p + 46p
-161 + 34p + 10p2 = -46p + 46p

Combine like terms: -46p + 46p = 0
-161 + 34p + 10p2 = 0

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

Divide each side by '10'.
-16.1 + 3.4p + p2 = 0.0

Move the constant term to the right:

Add '16.1' to each side of the equation.
-16.1 + 3.4p + 16.1 + p2 = 0.0 + 16.1

Reorder the terms:
-16.1 + 16.1 + 3.4p + p2 = 0.0 + 16.1

Combine like terms: -16.1 + 16.1 = 0.0
0.0 + 3.4p + p2 = 0.0 + 16.1
3.4p + p2 = 0.0 + 16.1

Combine like terms: 0.0 + 16.1 = 16.1
3.4p + p2 = 16.1

The p term is 3.4p.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4p + 2.89 + p2 = 16.1 + 2.89

Reorder the terms:
2.89 + 3.4p + p2 = 16.1 + 2.89

Combine like terms: 16.1 + 2.89 = 18.99
2.89 + 3.4p + p2 = 18.99

Factor a perfect square on the left side:
(p + 1.7)(p + 1.7) = 18.99

Calculate the square root of the right side: 4.357751714

Break this problem into two subproblems by setting 
(p + 1.7) equal to 4.357751714 and -4.357751714.

Subproblem 1
p + 1.7 = 4.357751714

Simplifying
p + 1.7 = 4.357751714

Reorder the terms:
1.7 + p = 4.357751714

Solving
1.7 + p = 4.357751714

Solving for variable 'p'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + p = 4.357751714 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + p = 4.357751714 + -1.7
p = 4.357751714 + -1.7

Combine like terms: 4.357751714 + -1.7 = 2.657751714
p = 2.657751714

Simplifying
p = 2.657751714

Subproblem 2
p + 1.7 = -4.357751714

Simplifying
p + 1.7 = -4.357751714

Reorder the terms:
1.7 + p = -4.357751714

Solving
1.7 + p = -4.357751714

Solving for variable 'p'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + p = -4.357751714 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + p = -4.357751714 + -1.7
p = -4.357751714 + -1.7

Combine like terms: -4.357751714 + -1.7 = -6.057751714
p = -6.057751714

Simplifying
p = -6.057751714

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.657751714, -6.057751714}