(4u-2w)(-30w+20u)=

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Solution for (4u-2w)(-30w+20u)= equation: 


Simplifying
(4u + -2w)(-30w + 20u) = 0

Reorder the terms:
(4u + -2w)(20u + -30w) = 0

Multiply (4u + -2w) * (20u + -30w)
(4u * (20u + -30w) + -2w * (20u + -30w)) = 0
((20u * 4u + -30w * 4u) + -2w * (20u + -30w)) = 0

Reorder the terms:
((-120uw + 80u2) + -2w * (20u + -30w)) = 0
((-120uw + 80u2) + -2w * (20u + -30w)) = 0
(-120uw + 80u2 + (20u * -2w + -30w * -2w)) = 0
(-120uw + 80u2 + (-40uw + 60w2)) = 0

Reorder the terms:
(-120uw + -40uw + 80u2 + 60w2) = 0

Combine like terms: -120uw + -40uw = -160uw
(-160uw + 80u2 + 60w2) = 0

Solving
-160uw + 80u2 + 60w2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-8uw + 4u2 + 3w2) = 0

Factor a trinomial.
20((2u + -3w)(2u + -1w)) = 0

Ignore the factor 20.

Subproblem 1
Set the factor '(2u + -3w)' equal to zero and attempt to solve:

Simplifying
2u + -3w = 0

Solving
2u + -3w = 0

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

Add '3w' to each side of the equation.
2u + -3w + 3w = 0 + 3w

Combine like terms: -3w + 3w = 0
2u + 0 = 0 + 3w
2u = 0 + 3w
Remove the zero:
2u = 3w

Divide each side by '2'.
u = 1.5w

Simplifying
u = 1.5w

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

Simplifying
2u + -1w = 0

Solving
2u + -1w = 0

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

Add 'w' to each side of the equation.
2u + -1w + w = 0 + w

Combine like terms: -1w + w = 0
2u + 0 = 0 + w
2u = 0 + w
Remove the zero:
2u = w

Divide each side by '2'.
u = 0.5w

Simplifying
u = 0.5w
Solution
u = {1.5w, 0.5w}

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