Question

Factoring Trinomials: Factor 12y^2=+17y-6

Answer 1

Quadratic formula: -b +/- √b² - 4ac
-------------------------
2a

First...

12y² = 17y - 6
- 12y² - 12y²
-----------------------------------
0 = -12y² + 17y -6


In the formula...

a = -12
b = 17
c = -6


Steps:

-17 +/- √(17)² - 4(-12)(-6) -17 +/- √289 - 4(72) -17 +/- √289 - 288
------------------------------ ⇒ ------------------------------ ⇒ ----------------------------
2(-12) -24 -24



-17 +/- √1 -17 + 1 -16 2 -17 -1 -18 3
------------------ ⇒ -------------- = -------- = ------- OR ----------- = ------- = ------
-24 -24 -24 3 - 24 -24 4




So x can equal 3/4 or 2/3. I'm sorry if my work seems confusing the way I typed it, but I hope this helps you at least a little bit.

Answer 2

Solve for y over the real numbers:
12 y^2 = 17 y - 6
Subtract 17 y - 6 from both sides:
12 y^2 - 17 y + 6 = 0
The left hand side factors into a product with two terms:
(3 y - 2) (4 y - 3) = 0
Split into two equations:
3 y - 2 = 0 or 4 y - 3 = 0
Add 2 to both sides:
3 y = 2 or 4 y - 3 = 0
Divide both sides by 3:
y = 2/3 or 4 y - 3 = 0
Add 3 to both sides:
y = 2/3 or 4 y = 3
Divide both sides by 4:
Answer: y = 2/3 or y = 3/4