(4z-u)(7z+7u)=

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Solution for (4z-u)(7z+7u)= equation: 


Simplifying
(4z + -1u)(7z + 7u) = 0

Reorder the terms:
(-1u + 4z)(7z + 7u) = 0

Reorder the terms:
(-1u + 4z)(7u + 7z) = 0

Multiply (-1u + 4z) * (7u + 7z)
(-1u * (7u + 7z) + 4z * (7u + 7z)) = 0
((7u * -1u + 7z * -1u) + 4z * (7u + 7z)) = 0

Reorder the terms:
((-7uz + -7u2) + 4z * (7u + 7z)) = 0
((-7uz + -7u2) + 4z * (7u + 7z)) = 0
(-7uz + -7u2 + (7u * 4z + 7z * 4z)) = 0
(-7uz + -7u2 + (28uz + 28z2)) = 0

Reorder the terms:
(-7uz + 28uz + -7u2 + 28z2) = 0

Combine like terms: -7uz + 28uz = 21uz
(21uz + -7u2 + 28z2) = 0

Solving
21uz + -7u2 + 28z2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '7'.
7(3uz + -1u2 + 4z2) = 0

Factor a trinomial.
7((-1u + -1z)(u + -4z)) = 0

Ignore the factor 7.

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

Simplifying
-1u + -1z = 0

Solving
-1u + -1z = 0

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

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

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

Divide each side by '-1'.
u = -1z

Simplifying
u = -1z

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 = {-1z, 4z}

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