( a-4)²-2a(5a-4) =-⅓

To solve the equation (a-4)²-2a(5a-4) = -1/3, you need to expand the squared term first:

(a-4)² = (a-4)(a-4) = a²-8a+16

Now, let's substitute this into the equation:

(a-4)²-2a(5a-4) = a²-8a+16-10a²+8a = -9a²

Now, equate this to -1/3:

-9a² = -1/3

To solve this equation, divide both sides by -9:

a² = 1/27

To find the value of a, take the square root of both sides:

a = ±√(1/27)

Simplifying the square root:

a = ±1/√27

Rationalizing the denominator (√27 = √(9*3) = 3√3):

a = ±1/(3√3)

Therefore, the solutions to the equation (a-4)²-2a(5a-4) = -1/3 are a = 1/(3√3) and a = -1/(3√3).