6y 2 −3y−4=y 2

The equation you've provided seems to be "6y^2 - 3y - 4 = y^2". Let's solve it step by step:

Step 1: Subtract y^2 from both sides to get the equation in standard form: 6y^2 - y^2 - 3y - 4 = 0 This simplifies to: 5y^2 - 3y - 4 = 0

Step 2: Now, we need to factor the equation. We're looking for two numbers that multiply to -20 (5*-4) and add to -3. Those numbers are -5 and 4. So, we can rewrite -3y as -5y + 4y: 5y^2 - 5y + 4y - 4 = 0

Step 3: Factor by grouping: 5y(y - 1) + 4(y - 1) = 0

Step 4: Now, you can see that (y - 1) is a common factor: (y - 1)(5y + 4) = 0

Step 5: Set each factor equal to zero and solve for y: y - 1 = 0 => y = 1 5y + 4 = 0 => y = -4/5

So, the solutions to the equation "6y^2 - 3y - 4 = y^2" are y = 1 and y = -4/5.