Final answer:
To solve the equation 5c² = 16c + 16, we can use factoring to simplify the expression and find the values of c. The solutions are c = 4 and c = -4/5.
Step-by-step explanation:
To solve the equation 5c² = 16c + 16, we can start by rearranging it to bring all the terms to one side:
5c² - 16c - 16 = 0
Next, we can factor the quadratic expression on the left-hand side:
(c - 4)(5c + 4) = 0
Using the zero product property, we set each factor equal to zero and solve for c:
c - 4 = 0, c = 4
5c + 4 = 0, c = -4/5
Therefore, the solutions to the equation are c = 4 and c = -4/5.