Question

Factoring 4p^2-10=3q

Answer 1

4p^2 - 10 = 3q
4p^2 - 3q - 10 = 0 - Subtract 3q from both sides
(4q + 5)(q - 2) = 0 - Factor both sides (I'll cover this at the end)
4q + 5 = 0    q - 2 = 0  - Find the answer one factor is zero for the whole thing to be 0
4q = -5         q = 2
q = -5/4

To factor the 4q^2 - 3q - 10
1.  Look at the second sign it is - so the signs in the factors nust be opposites
2.  What numbers multiply to 10 (10*1 and 5*2) and 4 (4*1 and 2*2)
3. Pick the combinations that have a difference of 3
This case 4*2 - 5*1 has a difference of 3 so these go into the opposite factors
(4q + 5)(q - 2) would not be our factors