x^4+r=(x^2+qx+8)(x^2+px+8)

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Solution for x^4+r=(x^2+qx+8)(x^2+px+8) equation: 


Simplifying
x4 + r = (x2 + qx + 8)(x2 + px + 8)

Reorder the terms:
r + x4 = (x2 + qx + 8)(x2 + px + 8)

Reorder the terms:
r + x4 = (8 + qx + x2)(x2 + px + 8)

Reorder the terms:
r + x4 = (8 + qx + x2)(8 + px + x2)

Multiply (8 + qx + x2) * (8 + px + x2)
r + x4 = (8(8 + px + x2) + qx(8 + px + x2) + x2(8 + px + x2))
r + x4 = ((8 * 8 + px * 8 + x2 * 8) + qx(8 + px + x2) + x2(8 + px + x2))
r + x4 = ((64 + 8px + 8x2) + qx(8 + px + x2) + x2(8 + px + x2))
r + x4 = (64 + 8px + 8x2 + (8 * qx + px * qx + x2 * qx) + x2(8 + px + x2))

Reorder the terms:
r + x4 = (64 + 8px + 8x2 + (pqx2 + 8qx + qx3) + x2(8 + px + x2))
r + x4 = (64 + 8px + 8x2 + (pqx2 + 8qx + qx3) + x2(8 + px + x2))
r + x4 = (64 + 8px + 8x2 + pqx2 + 8qx + qx3 + (8 * x2 + px * x2 + x2 * x2))

Reorder the terms:
r + x4 = (64 + 8px + 8x2 + pqx2 + 8qx + qx3 + (px3 + 8x2 + x4))
r + x4 = (64 + 8px + 8x2 + pqx2 + 8qx + qx3 + (px3 + 8x2 + x4))

Reorder the terms:
r + x4 = (64 + pqx2 + 8px + px3 + 8qx + qx3 + 8x2 + 8x2 + x4)

Combine like terms: 8x2 + 8x2 = 16x2
r + x4 = (64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2 + x4)

Add '-1x4' to each side of the equation.
r + x4 + -1x4 = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2 + x4 + -1x4

Combine like terms: x4 + -1x4 = 0
r + 0 = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2 + x4 + -1x4
r = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2 + x4 + -1x4

Combine like terms: x4 + -1x4 = 0
r = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2 + 0
r = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2

Solving
r = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2

Solving for variable 'r'.

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

Simplifying
r = 64 + pqx2 + 8px + px3 + 8qx + qx3 + 16x2

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