X²-4/8-2x+3/3=-1

To solve the equation x² - 4/8 - 2x + 3/3 = -1, we can follow these steps:

Step 1: Simplify the equation where possible. First, we need to find a common denominator for the fractions. The least common denominator (LCD) for 8 and 3 is 24. Let's multiply both sides of the equation by 24 to eliminate the fractions:

24(x² - 4/8 - 2x) + 24(3/3) = 24(-1)

Simplifying the equation further:

24x² - 12 - 48x + 24 + 24 = -24

Step 2: Combine like terms on both sides of the equation. Combining like terms on the left side:

24x² - 48x + 12 = -24

Step 3: Move all terms to one side of the equation to set it equal to zero. Subtracting -24 from both sides:

24x² - 48x + 36 = 0

Step 4: If possible, factor the polynomial. This equation can be factored as a perfect square trinomial:

(4x - 6)(6x - 6) = 0

Step 5: Set each factor equal to zero and solve for x. Setting (4x - 6) equal to zero:

4x - 6 = 0 4x = 6 x = 6/4 x = 3/2

Setting (6x - 6) equal to zero:

6x - 6 = 0 6x = 6 x = 6/6 x = 1

Therefore, the solutions for the equation x² - 4/8 - 2x + 3/3 = -1 are x = 3/2 and x = 1.