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

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


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

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

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

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

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

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

Combine like terms: -3uz + 35uz = 32uz
(32uz + -7u2 + 15z2) = 0

Solving
32uz + -7u2 + 15z2 = 0

Solving for variable 'u'.

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


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

Simplifying
-7u + -3z = 0

Solving
-7u + -3z = 0

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

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

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

Divide each side by '-7'.
u = -0.4285714286z

Simplifying
u = -0.4285714286z

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 = {-0.4285714286z, 5z}

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