(5u-5v)x(7u-6v)=

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Solution for (5u-5v)x(7u-6v)= equation: 


Simplifying
(5u + -5v) * x(7u + -6v) = 0

Reorder the terms for easier multiplication:
x(5u + -5v)(7u + -6v) = 0

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

Reorder the terms:
x((-30uv + 35u2) + -5v * (7u + -6v)) = 0
x((-30uv + 35u2) + -5v * (7u + -6v)) = 0
x(-30uv + 35u2 + (7u * -5v + -6v * -5v)) = 0
x(-30uv + 35u2 + (-35uv + 30v2)) = 0

Reorder the terms:
x(-30uv + -35uv + 35u2 + 30v2) = 0

Combine like terms: -30uv + -35uv = -65uv
x(-65uv + 35u2 + 30v2) = 0
(-65uv * x + 35u2 * x + 30v2 * x) = 0
(-65uvx + 35u2x + 30v2x) = 0

Solving
-65uvx + 35u2x + 30v2x = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-13uv + 7u2 + 6v2) = 0

Factor a trinomial.
5x((u + -1v)(7u + -6v)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
u + -1v = 0

Solving
u + -1v = 0

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

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

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

Simplifying
u = v

Subproblem 3
Set the factor '(7u + -6v)' equal to zero and attempt to solve:

Simplifying
7u + -6v = 0

Solving
7u + -6v = 0

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

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

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

Divide each side by '7'.
u = 0.8571428571v

Simplifying
u = 0.8571428571v
Solution
u = {v, 0.8571428571v}

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