Factoring 4p^2-10=3q

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