4t-13t-12=

Question

i want to factor the equation

Answer 1

I'm going to assume that this was entered in wrong and that you meant:

4t²-13t-12 = 0

This is a quadratic equation of the form:

ax²+bx+c = 0

The factored solution in this case would be:

(a₁t+c₁)(a₂t+c₂)

a = 4 and is the product (a₁*a₂) so that the factors a₁ and a₂ must be (1*4) or (2*2) and are both positive

c = -12 and is the product (c₁*c₂) so that the factors c₁ and c₂ must be

(1*12), (2*6), or (3*4) where one factor is negative and the other is positive

b = -13 and is a sum of products meaning that the factors of a and c have to be cross multiplied and add up to -13:

(a₁*c₂)+(a₂*c₁) = -13

The only case for b = -13 has 4*-4 = -16 and 1*3 = 3

Your answer is: (4t+3)(t-4)