u^2+2ux+x^2=0

Solution for u^2+2ux+x^2=0 equation:

Simplifying
u2 + 2ux + x2 = 0

Reorder the terms:
2ux + u2 + x2 = 0

Solving
2ux + u2 + x2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + x)(u + x) = 0

Subproblem 1
Set the factor '(u + x)' equal to zero and attempt to solve:

Simplifying
u + x = 0

Solving
u + x = 0

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

Add '-1x' to each side of the equation.
u + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
u + 0 = 0 + -1x
u = 0 + -1x
Remove the zero:
u = -1x

Simplifying
u = -1x
Subproblem 2
Set the factor '(u + x)' equal to zero and attempt to solve:

Simplifying
u + x = 0

Solving
u + x = 0

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

Add '-1x' to each side of the equation.
u + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
u + 0 = 0 + -1x
u = 0 + -1x
Remove the zero:
u = -1x

Simplifying
u = -1x
Solution
u = {-1x, -1x}