(4u-5v)(2u+5v)=

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Solution for (4u-5v)(2u+5v)= equation: 


Simplifying
(4u + -5v)(2u + 5v) = 0

Multiply (4u + -5v) * (2u + 5v)
(4u * (2u + 5v) + -5v * (2u + 5v)) = 0
((2u * 4u + 5v * 4u) + -5v * (2u + 5v)) = 0

Reorder the terms:
((20uv + 8u2) + -5v * (2u + 5v)) = 0
((20uv + 8u2) + -5v * (2u + 5v)) = 0
(20uv + 8u2 + (2u * -5v + 5v * -5v)) = 0
(20uv + 8u2 + (-10uv + -25v2)) = 0

Reorder the terms:
(20uv + -10uv + 8u2 + -25v2) = 0

Combine like terms: 20uv + -10uv = 10uv
(10uv + 8u2 + -25v2) = 0

Solving
10uv + 8u2 + -25v2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4u + -5v)(2u + 5v) = 0


Subproblem 1
Set the factor '(4u + -5v)' equal to zero and attempt to solve:

Simplifying
4u + -5v = 0

Solving
4u + -5v = 0

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

Add '5v' to each side of the equation.
4u + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
4u + 0 = 0 + 5v
4u = 0 + 5v
Remove the zero:
4u = 5v

Divide each side by '4'.
u = 1.25v

Simplifying
u = 1.25v

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

Simplifying
2u + 5v = 0

Solving
2u + 5v = 0

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

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

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

Divide each side by '2'.
u = -2.5v

Simplifying
u = -2.5v
Solution
u = {1.25v, -2.5v}

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