(6z-u)(7z+4u)=0

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Solution for (6z-u)(7z+4u)=0 equation: 


Simplifying
(6z + -1u)(7z + 4u) = 0

Reorder the terms:
(-1u + 6z)(7z + 4u) = 0

Reorder the terms:
(-1u + 6z)(4u + 7z) = 0

Multiply (-1u + 6z) * (4u + 7z)
(-1u * (4u + 7z) + 6z * (4u + 7z)) = 0
((4u * -1u + 7z * -1u) + 6z * (4u + 7z)) = 0

Reorder the terms:
((-7uz + -4u2) + 6z * (4u + 7z)) = 0
((-7uz + -4u2) + 6z * (4u + 7z)) = 0
(-7uz + -4u2 + (4u * 6z + 7z * 6z)) = 0
(-7uz + -4u2 + (24uz + 42z2)) = 0

Reorder the terms:
(-7uz + 24uz + -4u2 + 42z2) = 0

Combine like terms: -7uz + 24uz = 17uz
(17uz + -4u2 + 42z2) = 0

Solving
17uz + -4u2 + 42z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-4u + -7z)(u + -6z) = 0


Subproblem 1
Set the factor '(-4u + -7z)' equal to zero and attempt to solve:

Simplifying
-4u + -7z = 0

Solving
-4u + -7z = 0

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

Add '7z' to each side of the equation.
-4u + -7z + 7z = 0 + 7z

Combine like terms: -7z + 7z = 0
-4u + 0 = 0 + 7z
-4u = 0 + 7z
Remove the zero:
-4u = 7z

Divide each side by '-4'.
u = -1.75z

Simplifying
u = -1.75z

Subproblem 2
Set the factor '(u + -6z)' equal to zero and attempt to solve:

Simplifying
u + -6z = 0

Solving
u + -6z = 0

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

Add '6z' to each side of the equation.
u + -6z + 6z = 0 + 6z

Combine like terms: -6z + 6z = 0
u + 0 = 0 + 6z
u = 0 + 6z
Remove the zero:
u = 6z

Simplifying
u = 6z
Solution
u = {-1.75z, 6z}

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