-6p+7=(2p-9)(40+-16p)

Solution for -6p+7=(2p-9)(40+-16p) equation:

Simplifying
-6p + 7 = (2p + -9)(40 + -16p)

Reorder the terms:
7 + -6p = (2p + -9)(40 + -16p)

Reorder the terms:
7 + -6p = (-9 + 2p)(40 + -16p)

Multiply (-9 + 2p) * (40 + -16p)
7 + -6p = (-9(40 + -16p) + 2p * (40 + -16p))
7 + -6p = ((40 * -9 + -16p * -9) + 2p * (40 + -16p))
7 + -6p = ((-360 + 144p) + 2p * (40 + -16p))
7 + -6p = (-360 + 144p + (40 * 2p + -16p * 2p))
7 + -6p = (-360 + 144p + (80p + -32p2))

Combine like terms: 144p + 80p = 224p
7 + -6p = (-360 + 224p + -32p2)

Solving
7 + -6p = -360 + 224p + -32p2

Solving for variable 'p'.

Reorder the terms:
7 + 360 + -6p + -224p + 32p2 = -360 + 224p + -32p2 + 360 + -224p + 32p2

Combine like terms: 7 + 360 = 367
367 + -6p + -224p + 32p2 = -360 + 224p + -32p2 + 360 + -224p + 32p2

Combine like terms: -6p + -224p = -230p
367 + -230p + 32p2 = -360 + 224p + -32p2 + 360 + -224p + 32p2

Reorder the terms:
367 + -230p + 32p2 = -360 + 360 + 224p + -224p + -32p2 + 32p2

Combine like terms: -360 + 360 = 0
367 + -230p + 32p2 = 0 + 224p + -224p + -32p2 + 32p2
367 + -230p + 32p2 = 224p + -224p + -32p2 + 32p2

Combine like terms: 224p + -224p = 0
367 + -230p + 32p2 = 0 + -32p2 + 32p2
367 + -230p + 32p2 = -32p2 + 32p2

Combine like terms: -32p2 + 32p2 = 0
367 + -230p + 32p2 = 0

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

Divide each side by '32'.
11.46875 + -7.1875p + p2 = 0

Move the constant term to the right:

Add '-11.46875' to each side of the equation.
11.46875 + -7.1875p + -11.46875 + p2 = 0 + -11.46875

Reorder the terms:
11.46875 + -11.46875 + -7.1875p + p2 = 0 + -11.46875

Combine like terms: 11.46875 + -11.46875 = 0.00000
0.00000 + -7.1875p + p2 = 0 + -11.46875
-7.1875p + p2 = 0 + -11.46875

Combine like terms: 0 + -11.46875 = -11.46875
-7.1875p + p2 = -11.46875

The p term is -7.1875p.  Take half its coefficient (-3.59375).
Square it (12.91503906) and add it to both sides.

Add '12.91503906' to each side of the equation.
-7.1875p + 12.91503906 + p2 = -11.46875 + 12.91503906

Reorder the terms:
12.91503906 + -7.1875p + p2 = -11.46875 + 12.91503906

Combine like terms: -11.46875 + 12.91503906 = 1.44628906
12.91503906 + -7.1875p + p2 = 1.44628906

Factor a perfect square on the left side:
(p + -3.59375)(p + -3.59375) = 1.44628906

Calculate the square root of the right side: 1.202617587

Break this problem into two subproblems by setting 
(p + -3.59375) equal to 1.202617587 and -1.202617587.

Subproblem 1
p + -3.59375 = 1.202617587

Simplifying
p + -3.59375 = 1.202617587

Reorder the terms:
-3.59375 + p = 1.202617587

Solving
-3.59375 + p = 1.202617587

Solving for variable 'p'.

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

Add '3.59375' to each side of the equation.
-3.59375 + 3.59375 + p = 1.202617587 + 3.59375

Combine like terms: -3.59375 + 3.59375 = 0.00000
0.00000 + p = 1.202617587 + 3.59375
p = 1.202617587 + 3.59375

Combine like terms: 1.202617587 + 3.59375 = 4.796367587
p = 4.796367587

Simplifying
p = 4.796367587

Subproblem 2
p + -3.59375 = -1.202617587

Simplifying
p + -3.59375 = -1.202617587

Reorder the terms:
-3.59375 + p = -1.202617587

Solving
-3.59375 + p = -1.202617587

Solving for variable 'p'.

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

Add '3.59375' to each side of the equation.
-3.59375 + 3.59375 + p = -1.202617587 + 3.59375

Combine like terms: -3.59375 + 3.59375 = 0.00000
0.00000 + p = -1.202617587 + 3.59375
p = -1.202617587 + 3.59375

Combine like terms: -1.202617587 + 3.59375 = 2.391132413
p = 2.391132413

Simplifying
p = 2.391132413

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.796367587, 2.391132413}