( a-4)²-2a(5a-4) =-⅓

To solve the expression, let's simplify step by step:

(a-4)² - 2a(5a-4)

First, let's expand the squared term: (a-4)² = (a-4)(a-4) = a² - 4a - 4a + 16 = a² - 8a + 16

Now, let's distribute the -2a to the terms inside the brackets: -2a(5a-4) = -10a² + 8a

Now, substitute the simplified values back into the expression: (a-4)² - 2a(5a-4) becomes: (a² - 8a + 16) - (-10a² + 8a)

Next, distribute the negative sign to the terms inside the brackets: (a² - 8a + 16) + 10a² - 8a

Now, combine like terms: a² + 10a² - 8a - 8a + 16

Combine the like terms further: 11a² - 16a + 16

Now, set the expression equal to -⅓ and solve for 'a': 11a² - 16a + 16 = -⅓

Since this is a quadratic equation, we need to rearrange it to set it equal to zero: 11a² - 16a + 16 + ⅓ = 0

Now, we can solve it by factoring, completing the square, or using the quadratic formula. However, the result you provided (-⅓) doesn't seem to match with the equation. Please double-check your question or equation.