(u-2v)(u+3v)=

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Solution for (u-2v)(u+3v)= equation: 


Simplifying
(u + -2v)(u + 3v) = 0

Multiply (u + -2v) * (u + 3v)
(u(u + 3v) + -2v * (u + 3v)) = 0
((u * u + 3v * u) + -2v * (u + 3v)) = 0

Reorder the terms:
((3uv + u2) + -2v * (u + 3v)) = 0
((3uv + u2) + -2v * (u + 3v)) = 0
(3uv + u2 + (u * -2v + 3v * -2v)) = 0
(3uv + u2 + (-2uv + -6v2)) = 0

Reorder the terms:
(3uv + -2uv + u2 + -6v2) = 0

Combine like terms: 3uv + -2uv = 1uv
(1uv + u2 + -6v2) = 0

Solving
1uv + u2 + -6v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -2v)(u + 3v) = 0


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

Simplifying
u + -2v = 0

Solving
u + -2v = 0

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

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

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

Simplifying
u = 2v

Subproblem 2
Set the factor '(u + 3v)' equal to zero and attempt to solve:

Simplifying
u + 3v = 0

Solving
u + 3v = 0

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

Add '-3v' to each side of the equation.
u + 3v + -3v = 0 + -3v

Combine like terms: 3v + -3v = 0
u + 0 = 0 + -3v
u = 0 + -3v
Remove the zero:
u = -3v

Simplifying
u = -3v
Solution
u = {2v, -3v}

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