3х-2)*3х+2)+4х-5)в квадрате=10х+21

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вопрос

Let's simplify the given expression and then equate it to 10x + 21:

(3x - 2)*(3x + 2) + (4x - 5) = 10x + 21

Expanding the left side of the equation:
(9x^2 - 6x + 6x - 4) + 4x - 5 = 10x + 21
(9x^2 - 4) + 4x - 5 = 10x + 21
9x^2 + 4x - 9 = 10x + 21

Now, moving all terms to one side:
9x^2 + 4x - 9 - 10x - 21 = 0
9x^2 - 6x - 30 = 0

Now, we have a quadratic equation. Let's solve it by factoring or using the quadratic formula:

The factors of 9x^2 are (3x)(3x) or (9x)(x)
The factors of -30 that add up to -6 are -10 and 4

Therefore, the equation becomes:
(3x - 10)(3x + 4) = 0

From here, we can solve for x by setting each factor to zero:
3x - 10 = 0
3x = 10
x = 10/3

and

3x + 4 = 0
3x = -4
x = -4/3

Therefore, the solution to the equation (3x - 2)*(3x + 2) + (4x - 5) = 10x + 21 is x = 10/3 or x = -4/3.