(6u+7v)(3u+5v)=0

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Solution for (6u+7v)(3u+5v)=0 equation: 


Simplifying
(6u + 7v)(3u + 5v) = 0

Multiply (6u + 7v) * (3u + 5v)
(6u * (3u + 5v) + 7v * (3u + 5v)) = 0
((3u * 6u + 5v * 6u) + 7v * (3u + 5v)) = 0

Reorder the terms:
((30uv + 18u2) + 7v * (3u + 5v)) = 0
((30uv + 18u2) + 7v * (3u + 5v)) = 0
(30uv + 18u2 + (3u * 7v + 5v * 7v)) = 0
(30uv + 18u2 + (21uv + 35v2)) = 0

Reorder the terms:
(30uv + 21uv + 18u2 + 35v2) = 0

Combine like terms: 30uv + 21uv = 51uv
(51uv + 18u2 + 35v2) = 0

Solving
51uv + 18u2 + 35v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(6u + 7v)(3u + 5v) = 0


Subproblem 1
Set the factor '(6u + 7v)' equal to zero and attempt to solve:

Simplifying
6u + 7v = 0

Solving
6u + 7v = 0

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

Add '-7v' to each side of the equation.
6u + 7v + -7v = 0 + -7v

Combine like terms: 7v + -7v = 0
6u + 0 = 0 + -7v
6u = 0 + -7v
Remove the zero:
6u = -7v

Divide each side by '6'.
u = -1.166666667v

Simplifying
u = -1.166666667v

Subproblem 2
Set the factor '(3u + 5v)' equal to zero and attempt to solve:

Simplifying
3u + 5v = 0

Solving
3u + 5v = 0

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

Add '-5v' to each side of the equation.
3u + 5v + -5v = 0 + -5v

Combine like terms: 5v + -5v = 0
3u + 0 = 0 + -5v
3u = 0 + -5v
Remove the zero:
3u = -5v

Divide each side by '3'.
u = -1.666666667v

Simplifying
u = -1.666666667v
Solution
u = {-1.166666667v, -1.666666667v}

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