(5z-u)(7z+3u)=

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Solution for (5z-u)(7z+3u)= equation: 


Simplifying
(5z + -1u)(7z + 3u) = 0

Reorder the terms:
(-1u + 5z)(7z + 3u) = 0

Reorder the terms:
(-1u + 5z)(3u + 7z) = 0

Multiply (-1u + 5z) * (3u + 7z)
(-1u * (3u + 7z) + 5z * (3u + 7z)) = 0
((3u * -1u + 7z * -1u) + 5z * (3u + 7z)) = 0

Reorder the terms:
((-7uz + -3u2) + 5z * (3u + 7z)) = 0
((-7uz + -3u2) + 5z * (3u + 7z)) = 0
(-7uz + -3u2 + (3u * 5z + 7z * 5z)) = 0
(-7uz + -3u2 + (15uz + 35z2)) = 0

Reorder the terms:
(-7uz + 15uz + -3u2 + 35z2) = 0

Combine like terms: -7uz + 15uz = 8uz
(8uz + -3u2 + 35z2) = 0

Solving
8uz + -3u2 + 35z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3u + -7z)(u + -5z) = 0


Subproblem 1
Set the factor '(-3u + -7z)' equal to zero and attempt to solve:

Simplifying
-3u + -7z = 0

Solving
-3u + -7z = 0

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

Add '7z' to each side of the equation.
-3u + -7z + 7z = 0 + 7z

Combine like terms: -7z + 7z = 0
-3u + 0 = 0 + 7z
-3u = 0 + 7z
Remove the zero:
-3u = 7z

Divide each side by '-3'.
u = -2.333333333z

Simplifying
u = -2.333333333z

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

Simplifying
u + -5z = 0

Solving
u + -5z = 0

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

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

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

Simplifying
u = 5z
Solution
u = {-2.333333333z, 5z}

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