(2u-5xa)(u-xa)=0

Solution for (2u-5xa)(u-xa)=0 equation:

Simplifying
(2u + -5xa)(u + -1xa) = 0

Reorder the terms:
(-5ax + 2u)(u + -1xa) = 0

Reorder the terms:
(-5ax + 2u)(-1ax + u) = 0

Multiply (-5ax + 2u) * (-1ax + u)
(-5ax * (-1ax + u) + 2u * (-1ax + u)) = 0
((-1ax * -5ax + u * -5ax) + 2u * (-1ax + u)) = 0

Reorder the terms:
((-5aux + 5a2x2) + 2u * (-1ax + u)) = 0
((-5aux + 5a2x2) + 2u * (-1ax + u)) = 0
(-5aux + 5a2x2 + (-1ax * 2u + u * 2u)) = 0
(-5aux + 5a2x2 + (-2aux + 2u2)) = 0

Reorder the terms:
(-5aux + -2aux + 5a2x2 + 2u2) = 0

Combine like terms: -5aux + -2aux = -7aux
(-7aux + 5a2x2 + 2u2) = 0

Solving
-7aux + 5a2x2 + 2u2 = 0

Solving for variable 'a'.

Factor a trinomial.
(ax + -1u)(5ax + -2u) = 0

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

Simplifying
ax + -1u = 0

Solving
ax + -1u = 0

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

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

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

Divide each side by 'x'.
a = ux-1

Simplifying
a = ux-1
Subproblem 2
Set the factor '(5ax + -2u)' equal to zero and attempt to solve:

Simplifying
5ax + -2u = 0

Solving
5ax + -2u = 0

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

Add '2u' to each side of the equation.
5ax + -2u + 2u = 0 + 2u

Combine like terms: -2u + 2u = 0
5ax + 0 = 0 + 2u
5ax = 0 + 2u
Remove the zero:
5ax = 2u

Divide each side by '5x'.
a = 0.4ux-1

Simplifying
a = 0.4ux-1
Solution
a = {ux-1, 0.4ux-1}