V*O+Z*S=Z*Z(Z*Z+S*S+Z*Z)+Z*Z(Z*Z+Z*Z)+S(S*S+Z*Z)

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Solution for V*O+Z*S=Z*Z(Z*Z+S*S+Z*Z)+Z*Z(Z*Z+Z*Z)+S(S*S+Z*Z) equation:


Simplifying
V * O + Z * S = Z * Z(Z * Z + S * S + Z * Z) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply V * O
OV + Z * S = Z * Z(Z * Z + S * S + Z * Z) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply Z * S
OV + SZ = Z * Z(Z * Z + S * S + Z * Z) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply Z * Z
OV + SZ = Z * Z(Z2 + S * S + Z * Z) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply S * S
OV + SZ = Z * Z(Z2 + S2 + Z * Z) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply Z * Z
OV + SZ = Z * Z(Z2 + S2 + Z2) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Reorder the terms:
OV + SZ = Z * Z(S2 + Z2 + Z2) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Combine like terms: Z2 + Z2 = 2Z2
OV + SZ = Z * Z(S2 + 2Z2) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply Z * Z
OV + SZ = Z2(S2 + 2Z2) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)
OV + SZ = (S2 * Z2 + 2Z2 * Z2) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)
OV + SZ = (S2Z2 + 2Z4) + Z * Z(Z * Z + Z * Z) + S(S * S + Z * Z)

Multiply Z * Z
OV + SZ = S2Z2 + 2Z4 + Z * Z(Z2 + Z * Z) + S(S * S + Z * Z)

Multiply Z * Z
OV + SZ = S2Z2 + 2Z4 + Z * Z(Z2 + Z2) + S(S * S + Z * Z)

Combine like terms: Z2 + Z2 = 2Z2
OV + SZ = S2Z2 + 2Z4 + Z * Z(2Z2) + S(S * S + Z * Z)

Remove parenthesis around (2Z2)
OV + SZ = S2Z2 + 2Z4 + Z * Z * 2Z2 + S(S * S + Z * Z)

Reorder the terms for easier multiplication:
OV + SZ = S2Z2 + 2Z4 + 2Z * Z * Z2 + S(S * S + Z * Z)

Multiply Z * Z
OV + SZ = S2Z2 + 2Z4 + 2Z2 * Z2 + S(S * S + Z * Z)

Multiply Z2 * Z2
OV + SZ = S2Z2 + 2Z4 + 2Z4 + S(S * S + Z * Z)

Multiply S * S
OV + SZ = S2Z2 + 2Z4 + 2Z4 + S(S2 + Z * Z)

Multiply Z * Z
OV + SZ = S2Z2 + 2Z4 + 2Z4 + S(S2 + Z2)
OV + SZ = S2Z2 + 2Z4 + 2Z4 + (S2 * S + Z2 * S)

Reorder the terms:
OV + SZ = S2Z2 + 2Z4 + 2Z4 + (SZ2 + S3)
OV + SZ = S2Z2 + 2Z4 + 2Z4 + (SZ2 + S3)

Reorder the terms:
OV + SZ = SZ2 + S2Z2 + S3 + 2Z4 + 2Z4

Combine like terms: 2Z4 + 2Z4 = 4Z4
OV + SZ = SZ2 + S2Z2 + S3 + 4Z4

Solving
OV + SZ = SZ2 + S2Z2 + S3 + 4Z4

Solving for variable 'O'.

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

Add '-1SZ' to each side of the equation.
OV + SZ + -1SZ = SZ2 + S2Z2 + S3 + -1SZ + 4Z4

Combine like terms: SZ + -1SZ = 0
OV + 0 = SZ2 + S2Z2 + S3 + -1SZ + 4Z4
OV = SZ2 + S2Z2 + S3 + -1SZ + 4Z4

Reorder the terms:
OV = -1SZ + SZ2 + S2Z2 + S3 + 4Z4

Divide each side by 'V'.
O = -1SV-1Z + SV-1Z2 + S2V-1Z2 + S3V-1 + 4V-1Z4

Simplifying
O = -1SV-1Z + SV-1Z2 + S2V-1Z2 + S3V-1 + 4V-1Z4

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