Question

solve the equation,
$(t - 3)(t + 2) = -4$
the solution set is .

Explanation:

Step1: Expand left-hand side

$(t-3)(t+2) = t^2 + 2t - 3t - 6 = t^2 - t - 6$

Step2: Rearrange to standard quadratic form

$t^2 - t - 6 = -4$
$t^2 - t - 6 + 4 = 0$
$t^2 - t - 2 = 0$

Step3: Factor the quadratic

$(t-2)(t+1) = 0$

Step4: Solve for t

Set each factor equal to 0:
$t-2=0 \implies t=2$
$t+1=0 \implies t=-1$

Answer:

$\{ -1, 2 \}$