Exponents and Polynomials
Solving an equation written in factored form
Solve.
\[
(y+6)(y-8)=0
\]
(If there is more than one solution, separate them with commas.)
Answer
The solutions to the equation are \(\boxed{-6, 8}\).
Step 1 ：The equation is already in factored form. To find the solutions, we need to set each factor equal to zero and solve for y. This is because if either factor is zero, the entire equation will be zero, which is the definition of a solution to the equation.
Step 2 ：Setting the first factor equal to zero gives us the equation \(y + 6 = 0\). Solving for y gives us the solution \(-6\).
Step 3 ：Setting the second factor equal to zero gives us the equation \(y - 8 = 0\). Solving for y gives us the solution \(8\).
Step 4 ：The solutions to the equation are \(\boxed{-6, 8}\).
