Final answer:
The solution to the equation 9y^2 = 30y - 25 is y = 5/3 or y = 1 2/3.
Step-by-step explanation:
To solve the equation 9y^2 = 30y - 25, we first need to rearrange it into a quadratic equation. Start by subtracting 30y and adding 25 to both sides of the equation to get 9y^2 - 30y + 25 = 0. Then, factor the quadratic by finding two numbers that multiply to give 9 * 25 = 225 and add up to -30. The numbers are -15 and -15, so the factored form of the equation is (3y - 5)(3y - 5) = 0. Now, set each factor equal to zero and solve for y: 3y - 5 = 0. Adding 5 to both sides gives us 3y = 5, and finally, dividing both sides by 3 gives the solution y = 5/3 or y = 1 2/3.