(3-2x)(6x-1)=(2x-3)^2

Предыдущий
вопрос Следующий
вопрос

Expanding the left side of the equation:

(3-2x)(6x-1) = 18x - 3 - 12x^2 + 2x
= -12x^2 + 20x - 3

Expanding the right side of the equation:

(2x-3)^2 = (2x-3)(2x-3)
= 4x^2 - 6x - 6x + 9
= 4x^2 - 12x + 9

Setting the left side equal to the right side:

-12x^2 + 20x - 3 = 4x^2 - 12x + 9

Rearranging the equation:

-12x^2 + 20x - 3 = 4x^2 - 12x + 9
-12x^2 - 4x^2 + 20x + 12x - 3 - 9 = 0
-16x^2 + 32x - 12 = 0

Dividing by -4 to simplify:

4x^2 - 8x + 3 = 0

This is the quadratic equation that results from the given expression.