Explain how to balance the chemical equation, KClO3 ⟶ KCl + O2 and include all steps

The balance of chemical equation : 2KClO₃ ⟶ 2KCl + 3O₂

Equalization (balance) of chemical reactions can be done using variables. Steps in equalizing the reaction equation:  

Reaction

1. Coefficient

KClO₃ ⟶ aKCl + bO₂

2. Equation

K ⇒ left =1, right=a ⇒a=1

Cl⇒ left =1, right=a ⇒a=1

O ⇒ left = 3, right = 2b ⇒3=2b, b = 1.5

The equation turns into :

KClO₃ ⟶ KCl + 1.5O₂

multiplied by 2

2KClO₃ ⟶ 2KCl + 3O₂

93.2 ml + 3920 ml = 4013 ml total  

(93.2 ml) * (2.03 m) / (4013 ml) = 0.0471 m

the volume in in l of the diluted solution would be 0.0471 m.