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

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

Simplifying
5p(p + -4) + -1(2p + -3)(3p + 4) = 0

Reorder the terms:
5p(-4 + p) + -1(2p + -3)(3p + 4) = 0
(-4 * 5p + p * 5p) + -1(2p + -3)(3p + 4) = 0
(-20p + 5p2) + -1(2p + -3)(3p + 4) = 0

Reorder the terms:
-20p + 5p2 + -1(-3 + 2p)(3p + 4) = 0

Reorder the terms:
-20p + 5p2 + -1(-3 + 2p)(4 + 3p) = 0

Multiply (-3 + 2p) * (4 + 3p)
-20p + 5p2 + -1(-3(4 + 3p) + 2p * (4 + 3p)) = 0
-20p + 5p2 + -1((4 * -3 + 3p * -3) + 2p * (4 + 3p)) = 0
-20p + 5p2 + -1((-12 + -9p) + 2p * (4 + 3p)) = 0
-20p + 5p2 + -1(-12 + -9p + (4 * 2p + 3p * 2p)) = 0
-20p + 5p2 + -1(-12 + -9p + (8p + 6p2)) = 0

Combine like terms: -9p + 8p = -1p
-20p + 5p2 + -1(-12 + -1p + 6p2) = 0
-20p + 5p2 + (-12 * -1 + -1p * -1 + 6p2 * -1) = 0
-20p + 5p2 + (12 + 1p + -6p2) = 0

Reorder the terms:
12 + -20p + 1p + 5p2 + -6p2 = 0

Combine like terms: -20p + 1p = -19p
12 + -19p + 5p2 + -6p2 = 0

Combine like terms: 5p2 + -6p2 = -1p2
12 + -19p + -1p2 = 0

Solving
12 + -19p + -1p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-12 + 19p + p2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 19p + 12 + p2 = 0 + 12

Reorder the terms:
-12 + 12 + 19p + p2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 19p + p2 = 0 + 12
19p + p2 = 0 + 12

Combine like terms: 0 + 12 = 12
19p + p2 = 12

The p term is 19p.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19p + 90.25 + p2 = 12 + 90.25

Reorder the terms:
90.25 + 19p + p2 = 12 + 90.25

Combine like terms: 12 + 90.25 = 102.25
90.25 + 19p + p2 = 102.25

Factor a perfect square on the left side:
(p + 9.5)(p + 9.5) = 102.25

Calculate the square root of the right side: 10.111874208

Break this problem into two subproblems by setting 
(p + 9.5) equal to 10.111874208 and -10.111874208.

Subproblem 1
p + 9.5 = 10.111874208

Simplifying
p + 9.5 = 10.111874208

Reorder the terms:
9.5 + p = 10.111874208

Solving
9.5 + p = 10.111874208

Solving for variable 'p'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + p = 10.111874208 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + p = 10.111874208 + -9.5
p = 10.111874208 + -9.5

Combine like terms: 10.111874208 + -9.5 = 0.611874208
p = 0.611874208

Simplifying
p = 0.611874208

Subproblem 2
p + 9.5 = -10.111874208

Simplifying
p + 9.5 = -10.111874208

Reorder the terms:
9.5 + p = -10.111874208

Solving
9.5 + p = -10.111874208

Solving for variable 'p'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + p = -10.111874208 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + p = -10.111874208 + -9.5
p = -10.111874208 + -9.5

Combine like terms: -10.111874208 + -9.5 = -19.611874208
p = -19.611874208

Simplifying
p = -19.611874208

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.611874208, -19.611874208}