[4(p+2q)-5r][4(p+2q)+5r]=

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Solution for [4(p+2q)-5r][4(p+2q)+5r]= equation:


Simplifying
[4(p + 2q) + -5r][4(p + 2q) + 5r] = 0
[(p * 4 + 2q * 4) + -5r][4(p + 2q) + 5r] = 0
[(4p + 8q) + -5r][4(p + 2q) + 5r] = 0
[4p + 8q + -5r][(p * 4 + 2q * 4) + 5r] = 0
[4p + 8q + -5r][(4p + 8q) + 5r] = 0

Multiply [4p + 8q + -5r] * [4p + 8q + 5r]
[4p * [4p + 8q + 5r] + 8q * [4p + 8q + 5r] + -5r * [4p + 8q + 5r]] = 0
[[4p * 4p + 8q * 4p + 5r * 4p] + 8q * [4p + 8q + 5r] + -5r * [4p + 8q + 5r]] = 0

Reorder the terms:
[[32pq + 20pr + 16p2] + 8q * [4p + 8q + 5r] + -5r * [4p + 8q + 5r]] = 0
[[32pq + 20pr + 16p2] + 8q * [4p + 8q + 5r] + -5r * [4p + 8q + 5r]] = 0
[32pq + 20pr + 16p2 + [4p * 8q + 8q * 8q + 5r * 8q] + -5r * [4p + 8q + 5r]] = 0

Reorder the terms:
[32pq + 20pr + 16p2 + [32pq + 40qr + 64q2] + -5r * [4p + 8q + 5r]] = 0
[32pq + 20pr + 16p2 + [32pq + 40qr + 64q2] + -5r * [4p + 8q + 5r]] = 0
[32pq + 20pr + 16p2 + 32pq + 40qr + 64q2 + [4p * -5r + 8q * -5r + 5r * -5r]] = 0
[32pq + 20pr + 16p2 + 32pq + 40qr + 64q2 + [-20pr + -40qr + -25r2]] = 0

Reorder the terms:
[32pq + 32pq + 20pr + -20pr + 16p2 + 40qr + -40qr + 64q2 + -25r2] = 0

Combine like terms: 32pq + 32pq = 64pq
[64pq + 20pr + -20pr + 16p2 + 40qr + -40qr + 64q2 + -25r2] = 0

Combine like terms: 20pr + -20pr = 0
[64pq + 0 + 16p2 + 40qr + -40qr + 64q2 + -25r2] = 0
[64pq + 16p2 + 40qr + -40qr + 64q2 + -25r2] = 0

Combine like terms: 40qr + -40qr = 0
[64pq + 16p2 + 0 + 64q2 + -25r2] = 0
[64pq + 16p2 + 64q2 + -25r2] = 0

Solving
64pq + 16p2 + 64q2 + -25r2 = 0

Solving for variable 'p'.

The solution to this equation could not be determined.

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