Let's first expand out the left side of the equation:

(3x+2)² = (3x+2)(3x+2)
= 9x² + 6x + 6x + 4
= 9x² + 12x + 4

(4x-1)(4x+1) = 16x² - x + 4x - 1
= 16x² + 3x - 1

Now, let's add the two expanded expressions together:

9x² + 12x + 4 + 16x² + 3x - 1 = 25x² + 15x + 3

Now, let's expand out the right side of the equation:

(5x-1)² = (5x-1)(5x-1)
= 25x² - 5x - 5x + 1
= 25x² - 10x + 1

Now, let's compare the left and right sides of the equation:

25x² + 15x + 3 = 25x² - 10x + 1

Since this is not true, the original equation (3x+2)²+ (4x-1)(4x+1) does not equal (5x-1)².