(2x-1)^2 (x+5)=(4x+5) (x+1)^2 ПЖ

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To solve this equation, we can begin by expanding both sides of the equation:

Expanding the left side
(2x - 1)^2 * (x + 5
= (2x - 1)(2x - 1)(x + 5
= (4x^2 - 2x - 2x + 1)(x + 5
= (4x^2 - 4x + 1)(x + 5
= 4x^3 + 20x^2 - 4x^2 - 20x + x +
= 4x^3 + 16x^2 - 19x + 5

Expanding the right side
(4x + 5)(x + 1)^
= (4x + 5)(x^2 + 2x + 1
= 4x^3 + 8x^2 + 4x + 5x^2 + 10x +
= 4x^3 + 13x^2 + 14x + 5

Therefore, the equation becomes
4x^3 + 16x^2 - 19x + 5 = 4x^3 + 13x^2 + 14x + 5

Subtracting 4x^3 from both sides
16x^2 - 19x + 5 = 13x^2 + 14x + 5

Subtracting 13x^2 and 14x from both sides
3x^2 - 33x = 0

Factor out an x
x(3x - 33) = 0

Setting each factor to zero gives the solutions
x =
3x - 33 =
3x = 3
x = 11

Therefore, the solutions to the equation are x = 0 and x = 11.