12-х(х-3)=(6-х)(х+2) (1-2х)(1-3х)=(6х-1)х-1

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вопрос

To find the solution to the given equations, we will simplify each equation separately.

1) 12x(x-3) = (6-x)(x+2)
Expanding the left side:
12x^2 - 36x

Expanding the right side:
6x^2 + 12x - x^2 - 2x
6x^2 + 12x - x^2 - 2x
5x^2 + 10x

Now, equating the left and right sides:
12x^2 - 36x = 5x^2 + 10x

Rearranging the terms:
12x^2 - 5x^2 - 36x - 10x = 0
7x^2 - 46x = 0
x(7x - 46) = 0

Setting each factor to zero:
x = 0 or 7x - 46 = 0
x = 0 or x = 46/7

Therefore, the solutions to the first equation are x = 0 and x = (46/7).

2) (1-2x)(1-3x) = (6x-1)x - 1
Expanding the left side:
1 - 3x - 2x + 6x^2
1 - 5x + 6x^2

Expanding the right side:
6x^2 - x - 1
6x^2 - x - 1

Now, equating the left and right sides:
1 - 5x + 6x^2 = 6x^2 - x - 1
1 - 5x + 6x^2 = 6x^2 - x - 1

Subtracting the common terms:
-5x = -x - 2
-5x + x = -2
-4x = -2
x = -2/-4
x = 1/2

Therefore, the solution to the second equation is x = 1/2.

In conclusion, the solutions to the given equations are:
x = 0, x = 46/7, and x = 1/2.