Question

(x-3)(x-2)= 6x-18 решите уравнение

Answer 1

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Answer 2

To solve the equation (x-3)(x-2) = 6x-18, follow these steps:

Step 1: Expand the left side of the equation: (x-3)(x-2) = x^2 - 2x - 3x + 6

Step 2: Simplify the equation: x^2 - 5x + 6 = 6x - 18

Step 3: Move all terms to one side of the equation to set it to zero: x^2 - 5x - 6x + 18 - 6 = 0

Step 4: Combine like terms: x^2 - 11x + 12 = 0

Step 5: Factor the quadratic equation (or use any other method, such as the quadratic formula) to find the solutions for x:

The factored form of the equation is: (x - 3)(x - 4) = 0

Now, set each factor equal to zero and solve for x: x - 3 = 0 or x - 4 = 0

Solving for x in each case: For x - 3 = 0: x = 3

For x - 4 = 0: x = 4

So, the solutions to the equation are x = 3 and x = 4.