Solve for x if 4(2x+3)2−(2x+3)−14=0.
The correct option is A. x=−12,−198
Given: 4(2x+3)2−(2x+3)−14=0
Substitute (2x+3)=y, the given equation reduces to
4y2−y−14=0
Using Middle Term Splitting,
⇒ 4y2−8y+7y−14=0
⇒ 4y(y−2)+7(y−2)=0
⇒ (4y+7)(y−2)=0
⇒ y=−74 or y=2
When y=−74,
(2x+3)=−74
2x=−74−3=−7−124=−194
⇒ x=−198
When y=2,
(2x+3)=2
2x=−1
⇒ x=−12
Hence, x=−12,−198