(3p-q-r)(3p+q+r)=

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Solution for (3p-q-r)(3p+q+r)= equation: 


Simplifying
(3p + -1q + -1r)(3p + q + r) = 0

Multiply (3p + -1q + -1r) * (3p + q + r)
(3p * (3p + q + r) + -1q * (3p + q + r) + -1r * (3p + q + r)) = 0
((3p * 3p + q * 3p + r * 3p) + -1q * (3p + q + r) + -1r * (3p + q + r)) = 0

Reorder the terms:
((3pq + 3pr + 9p2) + -1q * (3p + q + r) + -1r * (3p + q + r)) = 0
((3pq + 3pr + 9p2) + -1q * (3p + q + r) + -1r * (3p + q + r)) = 0
(3pq + 3pr + 9p2 + (3p * -1q + q * -1q + r * -1q) + -1r * (3p + q + r)) = 0

Reorder the terms:
(3pq + 3pr + 9p2 + (-3pq + -1qr + -1q2) + -1r * (3p + q + r)) = 0
(3pq + 3pr + 9p2 + (-3pq + -1qr + -1q2) + -1r * (3p + q + r)) = 0
(3pq + 3pr + 9p2 + -3pq + -1qr + -1q2 + (3p * -1r + q * -1r + r * -1r)) = 0
(3pq + 3pr + 9p2 + -3pq + -1qr + -1q2 + (-3pr + -1qr + -1r2)) = 0

Reorder the terms:
(3pq + -3pq + 3pr + -3pr + 9p2 + -1qr + -1qr + -1q2 + -1r2) = 0

Combine like terms: 3pq + -3pq = 0
(0 + 3pr + -3pr + 9p2 + -1qr + -1qr + -1q2 + -1r2) = 0
(3pr + -3pr + 9p2 + -1qr + -1qr + -1q2 + -1r2) = 0

Combine like terms: 3pr + -3pr = 0
(0 + 9p2 + -1qr + -1qr + -1q2 + -1r2) = 0
(9p2 + -1qr + -1qr + -1q2 + -1r2) = 0

Combine like terms: -1qr + -1qr = -2qr
(9p2 + -2qr + -1q2 + -1r2) = 0

Solving
9p2 + -2qr + -1q2 + -1r2 = 0

Solving for variable 'p'.

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

Add '2qr' to each side of the equation.
9p2 + -2qr + -1q2 + 2qr + -1r2 = 0 + 2qr

Reorder the terms:
9p2 + -2qr + 2qr + -1q2 + -1r2 = 0 + 2qr

Combine like terms: -2qr + 2qr = 0
9p2 + 0 + -1q2 + -1r2 = 0 + 2qr
9p2 + -1q2 + -1r2 = 0 + 2qr
Remove the zero:
9p2 + -1q2 + -1r2 = 2qr

Add 'q2' to each side of the equation.
9p2 + -1q2 + q2 + -1r2 = 2qr + q2

Combine like terms: -1q2 + q2 = 0
9p2 + 0 + -1r2 = 2qr + q2
9p2 + -1r2 = 2qr + q2

Add 'r2' to each side of the equation.
9p2 + -1r2 + r2 = 2qr + q2 + r2

Combine like terms: -1r2 + r2 = 0
9p2 + 0 = 2qr + q2 + r2
9p2 = 2qr + q2 + r2

Divide each side by '9'.
p2 = 0.2222222222qr + 0.1111111111q2 + 0.1111111111r2

Simplifying
p2 = 0.2222222222qr + 0.1111111111q2 + 0.1111111111r2

Reorder the terms:
p2 + -0.2222222222qr + -0.1111111111q2 + -0.1111111111r2 = 0.2222222222qr + -0.2222222222qr + 0.1111111111q2 + -0.1111111111q2 + 0.1111111111r2 + -0.1111111111r2

Combine like terms: 0.2222222222qr + -0.2222222222qr = 0.0000000000
p2 + -0.2222222222qr + -0.1111111111q2 + -0.1111111111r2 = 0.0000000000 + 0.1111111111q2 + -0.1111111111q2 + 0.1111111111r2 + -0.1111111111r2
p2 + -0.2222222222qr + -0.1111111111q2 + -0.1111111111r2 = 0.1111111111q2 + -0.1111111111q2 + 0.1111111111r2 + -0.1111111111r2

Combine like terms: 0.1111111111q2 + -0.1111111111q2 = 0.0000000000
p2 + -0.2222222222qr + -0.1111111111q2 + -0.1111111111r2 = 0.0000000000 + 0.1111111111r2 + -0.1111111111r2
p2 + -0.2222222222qr + -0.1111111111q2 + -0.1111111111r2 = 0.1111111111r2 + -0.1111111111r2

Combine like terms: 0.1111111111r2 + -0.1111111111r2 = 0.0000000000
p2 + -0.2222222222qr + -0.1111111111q2 + -0.1111111111r2 = 0.0000000000

The solution to this equation could not be determined.

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