(4u+v)(4u-v)=

Solution for (4u+v)(4u-v)= equation:

Simplifying
(4u + v)(4u + -1v) = 0

Multiply (4u + v) * (4u + -1v)
(4u * (4u + -1v) + v(4u + -1v)) = 0
((4u * 4u + -1v * 4u) + v(4u + -1v)) = 0

Reorder the terms:
((-4uv + 16u2) + v(4u + -1v)) = 0
((-4uv + 16u2) + v(4u + -1v)) = 0
(-4uv + 16u2 + (4u * v + -1v * v)) = 0
(-4uv + 16u2 + (4uv + -1v2)) = 0

Reorder the terms:
(-4uv + 4uv + 16u2 + -1v2) = 0

Combine like terms: -4uv + 4uv = 0
(0 + 16u2 + -1v2) = 0
(16u2 + -1v2) = 0

Solving
16u2 + -1v2 = 0

Solving for variable 'u'.

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

Add 'v2' to each side of the equation.
16u2 + -1v2 + v2 = 0 + v2

Combine like terms: -1v2 + v2 = 0
16u2 + 0 = 0 + v2
16u2 = 0 + v2
Remove the zero:
16u2 = v2

Divide each side by '16'.
u2 = 0.0625v2

Simplifying
u2 = 0.0625v2

Take the square root of each side:
u = {-0.25v, 0.25v}