Question

(x - 3) (x - 2) = 6 (x - 3)​

Answer 1

Ответ:

x$x_1=3 ;x_2=8$

Пошаговое объяснение:

Answer 2

To solve the given equation $(x - 3)(x - 2) = 6(x - 3)$, we'll start by simplifying both sides of the equation and then solving for $x$:

Expand the left side: $(x - 3)(x - 2) = x^2 - 2x - 3x + 6 = x^2 - 5x + 6$

Expand the right side: $6(x - 3) = 6x - 18$

Now the equation becomes: $x^2 - 5x + 6 = 6x - 18$

Subtract $6x$ from both sides: $x^2 - 11x + 6 = -18$

Add $18$ to both sides: $x^2 - 11x + 24 = 0$

Now we have a quadratic equation. We can solve this quadratic equation by factoring or using the quadratic formula.

Factoring: We need to find two numbers that multiply to $24$ and add up to $-11$. Those numbers are $-8$ and $-3$: $(x - 8)(x - 3) = 0$

Setting each factor equal to $0$: $x - 8 = 0$ or $x - 3 = 0$

Solving for $x$: $x = 8$ or $x = 3$

So, the solutions to the equation are $x = 8$ and $x = 3$.