Final answer:
The equation y² = 6 - 5y is solved by rearranging it into standard quadratic form and factoring. The solutions are y = -6 or y = 1.
Step-by-step explanation:
To solve the equation y² = 6 - 5y, we need to rearrange it into a standard quadratic form, which is ax²+ bx + c = 0. First, move all terms to one side of the equation to get y² + 5y - 6 = 0.
Next, factor the quadratic equation to find the values of y that make the equation true. The factors of -6 that add up to 5 are 6 and -1. Therefore, the factored form of the equation is (y + 6)(y - 1) = 0. This indicates that y + 6 = 0 or y - 1 = 0. Solving for y, we get two possible solutions: y = -6 or y = 1.