Let |A→₁| = 3 , |A→₂| = 5 and |A→₁ + A→₂| = 5 . The value of (2 A→₁ + 3 A→₂) . (3 A→₁ - 2 A→₂) is :

Correct option is C. -118.5
|A→₁|=3
|A→₂|=5
|A→₁+A→₂|=5
|A→₁+A→₂|²=|A→₁|²+|A→₂|²+2|A→₁||A→₂|cosθ
25=9+25+2×3×5cosθ
cosθ=-9/(2×3×5)=-3/10
(2A→₁+3A→₂) . (3A→₁-2A→₂)=6|A→₁|²-4A→₁.A→₂+9A→₁.A→₂-6|A→₂|²
=6|A→₁|²+5A→₁.A→₂-6|A→₂|²
=6(9)+5(3)(5)(-3/10)-6(25)
=54+5(15)(-3/10)-150
=54-45/2-150
=54-22.5-150
=-118.5