(6u+v)(u-2v)=0

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Solution for (6u+v)(u-2v)=0 equation: 


Simplifying
(6u + v)(u + -2v) = 0

Multiply (6u + v) * (u + -2v)
(6u * (u + -2v) + v(u + -2v)) = 0
((u * 6u + -2v * 6u) + v(u + -2v)) = 0

Reorder the terms:
((-12uv + 6u2) + v(u + -2v)) = 0
((-12uv + 6u2) + v(u + -2v)) = 0
(-12uv + 6u2 + (u * v + -2v * v)) = 0
(-12uv + 6u2 + (uv + -2v2)) = 0

Reorder the terms:
(-12uv + uv + 6u2 + -2v2) = 0

Combine like terms: -12uv + uv = -11uv
(-11uv + 6u2 + -2v2) = 0

Solving
-11uv + 6u2 + -2v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(u + -2v)(6u + v) = 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 '(6u + v)' equal to zero and attempt to solve:

Simplifying
6u + v = 0

Solving
6u + v = 0

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

Add '-1v' to each side of the equation.
6u + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
6u + 0 = 0 + -1v
6u = 0 + -1v
Remove the zero:
6u = -1v

Divide each side by '6'.
u = -0.1666666667v

Simplifying
u = -0.1666666667v
Solution
u = {2v, -0.1666666667v}

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