Question

solve the equation.

\\e^{-6w-24} = e^{(3w-5)(w+4)}\\

\\(w =\\)

Explanation:

Step1: Equate the exponents

$$-6w - 24 = (3w - 5)(w + 4)$$

Step2: Expand the right side

$$-6w - 24 = 3w^2 + 12w - 5w - 20$$

Step3: Simplify the equation

$$-6w - 24 = 3w^2 + 7w - 20$$

Step4: Move all terms to one side

$$3w^2 + 13w + 4 = 0$$

Step5: Factor the quadratic equation

$$(3w + 1)(w + 4) = 0$$

Step6: Solve for \(w\)

$$w = -\frac{1}{3}, -4$$

Answer:

\(w = -4, \frac{1}{3}\)