(2x – 1)(x – 3) = (x + 5)(x – 1)

To solve the equation (2x – 1)(x – 3) = (x + 5)(x – 1), we can follow these steps:

Step 1: Expand both sides of the equation using the distributive property. (2x – 1)(x – 3) = (x + 5)(x – 1) 2x^2 - 6x - x + 3 = x^2 - x + 5x - 5

Step 2: Simplify the equation by combining like terms. 2x^2 - 7x + 3 = x^2 + 4x - 5

Step 3: Move all terms to one side of the equation to set it equal to zero. 2x^2 - 7x + 3 - x^2 - 4x + 5 = 0

Step 4: Combine like terms again. x^2 - 11x + 8 = 0

Step 5: Factor the quadratic equation. (x - 1)(x - 8) = 0

Step 6: Set each factor equal to zero and solve for x. x - 1 = 0 or x - 8 = 0 x = 1 or x = 8

Therefore, the solutions to the equation (2x – 1)(x – 3) = (x + 5)(x – 1) are x = 1 and x = 8.