(-4a+b)(4a+b)=0

Solution for (-4a+b)(4a+b)=0 equation:

Simplifying
(-4a + b)(4a + b) = 0

Multiply (-4a + b) * (4a + b)
(-4a * (4a + b) + b(4a + b)) = 0
((4a * -4a + b * -4a) + b(4a + b)) = 0

Reorder the terms:
((-4ab + -16a2) + b(4a + b)) = 0
((-4ab + -16a2) + b(4a + b)) = 0
(-4ab + -16a2 + (4a * b + b * b)) = 0
(-4ab + -16a2 + (4ab + b2)) = 0

Reorder the terms:
(-4ab + 4ab + -16a2 + b2) = 0

Combine like terms: -4ab + 4ab = 0
(0 + -16a2 + b2) = 0
(-16a2 + b2) = 0

Solving
-16a2 + b2 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1b2' to each side of the equation.
-16a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
-16a2 + 0 = 0 + -1b2
-16a2 = 0 + -1b2
Remove the zero:
-16a2 = -1b2

Divide each side by '-16'.
a2 = 0.0625b2

Simplifying
a2 = 0.0625b2

Take the square root of each side:
a = {-0.25b, 0.25b}