Question

Решите уравнение (3z - 2)(5z + 3) - (2z - 1)(7z + 2) = -4.

Answer 1

Ответ:

(3z-2)(5z+3)-(2z-1)(7z+2)=-4

15z^2+9z-10z-6-14z^2-4z+7z+2+4=0

z^2+2z=0

z(z+2)=0

z=0 или z= -2

Ответ : 0;-2

Answer 2

To solve the given equation, let's first expand the expressions and then simplify the equation:

(3z - 2)(5z + 3) - (2z - 1)(7z + 2) = -4

Expanding the expressions inside the brackets:

(3z * 5z) + (3z * 3) - (2 * 5z) - (2 * 3) - (2z * 7z) - (2z * 2) + (1 * 7z) + (1 * 2) = -4

Now, simplify the equation further:

15z^2 + 9z - 10z - 6 - 14z^2 - 4z + 7z + 2 = -4

Combine like terms:

15z^2 - 5z - 4 = -4

Next, move all terms to one side of the equation to make it equal to zero:

15z^2 - 5z - 4 + 4 = 0

15z^2 - 5z = 0

Now, we can factor out the common term (5z):

5z(3z - 1) = 0

Now set each factor equal to zero and solve for 'z':

1. 5z = 0 z = 0

2. 3z - 1 = 0 3z = 1 z = 1/3

So, the solutions to the equation are z = 0 and z = 1/3.