(4z-u)(5z+3u)=

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Solution for (4z-u)(5z+3u)= equation: 


Simplifying
(4z + -1u)(5z + 3u) = 0

Reorder the terms:
(-1u + 4z)(5z + 3u) = 0

Reorder the terms:
(-1u + 4z)(3u + 5z) = 0

Multiply (-1u + 4z) * (3u + 5z)
(-1u * (3u + 5z) + 4z * (3u + 5z)) = 0
((3u * -1u + 5z * -1u) + 4z * (3u + 5z)) = 0

Reorder the terms:
((-5uz + -3u2) + 4z * (3u + 5z)) = 0
((-5uz + -3u2) + 4z * (3u + 5z)) = 0
(-5uz + -3u2 + (3u * 4z + 5z * 4z)) = 0
(-5uz + -3u2 + (12uz + 20z2)) = 0

Reorder the terms:
(-5uz + 12uz + -3u2 + 20z2) = 0

Combine like terms: -5uz + 12uz = 7uz
(7uz + -3u2 + 20z2) = 0

Solving
7uz + -3u2 + 20z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3u + -5z)(u + -4z) = 0


Subproblem 1
Set the factor '(-3u + -5z)' equal to zero and attempt to solve:

Simplifying
-3u + -5z = 0

Solving
-3u + -5z = 0

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

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

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

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

Simplifying
u = -1.666666667z

Subproblem 2
Set the factor '(u + -4z)' equal to zero and attempt to solve:

Simplifying
u + -4z = 0

Solving
u + -4z = 0

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

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

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

Simplifying
u = 4z
Solution
u = {-1.666666667z, 4z}

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