(p+1)(q+1)-3p(1-q)+2p(1+3q)=(p-q)(p+1)+10pq-p^2

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Solution for (p+1)(q+1)-3p(1-q)+2p(1+3q)=(p-q)(p+1)+10pq-p^2 equation: 


Simplifying
(p + 1)(q + 1) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2

Reorder the terms:
(1 + p)(q + 1) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2

Reorder the terms:
(1 + p)(1 + q) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2

Multiply (1 + p) * (1 + q)
(1(1 + q) + p(1 + q)) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
((1 * 1 + q * 1) + p(1 + q)) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
((1 + 1q) + p(1 + q)) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
(1 + 1q + (1 * p + q * p)) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
(1 + 1q + (1p + pq)) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2

Reorder the terms:
(1 + 1p + pq + 1q) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
(1 + 1p + pq + 1q) + -3p(1 + -1q) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
1 + 1p + pq + 1q + (1 * -3p + -1q * -3p) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
1 + 1p + pq + 1q + (-3p + 3pq) + 2p(1 + 3q) = (p + -1q)(p + 1) + 10pq + -1p2
1 + 1p + pq + 1q + -3p + 3pq + (1 * 2p + 3q * 2p) = (p + -1q)(p + 1) + 10pq + -1p2
1 + 1p + pq + 1q + -3p + 3pq + (2p + 6pq) = (p + -1q)(p + 1) + 10pq + -1p2

Reorder the terms:
1 + 1p + -3p + 2p + pq + 3pq + 6pq + 1q = (p + -1q)(p + 1) + 10pq + -1p2

Combine like terms: 1p + -3p = -2p
1 + -2p + 2p + pq + 3pq + 6pq + 1q = (p + -1q)(p + 1) + 10pq + -1p2

Combine like terms: -2p + 2p = 0
1 + 0 + pq + 3pq + 6pq + 1q = (p + -1q)(p + 1) + 10pq + -1p2
1 + pq + 3pq + 6pq + 1q = (p + -1q)(p + 1) + 10pq + -1p2

Combine like terms: pq + 3pq = 4pq
1 + 4pq + 6pq + 1q = (p + -1q)(p + 1) + 10pq + -1p2

Combine like terms: 4pq + 6pq = 10pq
1 + 10pq + 1q = (p + -1q)(p + 1) + 10pq + -1p2

Reorder the terms:
1 + 10pq + 1q = (p + -1q)(1 + p) + 10pq + -1p2

Multiply (p + -1q) * (1 + p)
1 + 10pq + 1q = (p(1 + p) + -1q * (1 + p)) + 10pq + -1p2
1 + 10pq + 1q = ((1 * p + p * p) + -1q * (1 + p)) + 10pq + -1p2
1 + 10pq + 1q = ((1p + p2) + -1q * (1 + p)) + 10pq + -1p2
1 + 10pq + 1q = (1p + p2 + (1 * -1q + p * -1q)) + 10pq + -1p2

Reorder the terms:
1 + 10pq + 1q = (1p + p2 + (-1pq + -1q)) + 10pq + -1p2
1 + 10pq + 1q = (1p + p2 + (-1pq + -1q)) + 10pq + -1p2

Reorder the terms:
1 + 10pq + 1q = (1p + -1pq + p2 + -1q) + 10pq + -1p2
1 + 10pq + 1q = (1p + -1pq + p2 + -1q) + 10pq + -1p2

Reorder the terms:
1 + 10pq + 1q = 1p + -1pq + 10pq + p2 + -1p2 + -1q

Combine like terms: -1pq + 10pq = 9pq
1 + 10pq + 1q = 1p + 9pq + p2 + -1p2 + -1q

Combine like terms: p2 + -1p2 = 0
1 + 10pq + 1q = 1p + 9pq + 0 + -1q
1 + 10pq + 1q = 1p + 9pq + -1q

Solving
1 + 10pq + 1q = 1p + 9pq + -1q

Solving for variable 'p'.

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

Add '-1p' to each side of the equation.
1 + 10pq + -1p + 1q = 1p + 9pq + -1p + -1q

Reorder the terms:
1 + -1p + 10pq + 1q = 1p + 9pq + -1p + -1q

Reorder the terms:
1 + -1p + 10pq + 1q = 1p + -1p + 9pq + -1q

Combine like terms: 1p + -1p = 0
1 + -1p + 10pq + 1q = 0 + 9pq + -1q
1 + -1p + 10pq + 1q = 9pq + -1q

Add '-9pq' to each side of the equation.
1 + -1p + 10pq + -9pq + 1q = 9pq + -9pq + -1q

Combine like terms: 10pq + -9pq = 1pq
1 + -1p + 1pq + 1q = 9pq + -9pq + -1q

Combine like terms: 9pq + -9pq = 0
1 + -1p + 1pq + 1q = 0 + -1q
1 + -1p + 1pq + 1q = -1q

Add '-1' to each side of the equation.
1 + -1p + 1pq + -1 + 1q = -1 + -1q

Reorder the terms:
1 + -1 + -1p + 1pq + 1q = -1 + -1q

Combine like terms: 1 + -1 = 0
0 + -1p + 1pq + 1q = -1 + -1q
-1p + 1pq + 1q = -1 + -1q

Add '-1q' to each side of the equation.
-1p + 1pq + 1q + -1q = -1 + -1q + -1q

Combine like terms: 1q + -1q = 0
-1p + 1pq + 0 = -1 + -1q + -1q
-1p + 1pq = -1 + -1q + -1q

Combine like terms: -1q + -1q = -2q
-1p + 1pq = -1 + -2q

Reorder the terms:
1 + -1p + 1pq + 2q = -1 + -2q + 1 + 2q

Reorder the terms:
1 + -1p + 1pq + 2q = -1 + 1 + -2q + 2q

Combine like terms: -1 + 1 = 0
1 + -1p + 1pq + 2q = 0 + -2q + 2q
1 + -1p + 1pq + 2q = -2q + 2q

Combine like terms: -2q + 2q = 0
1 + -1p + 1pq + 2q = 0

The solution to this equation could not be determined.

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