(9z+-1u)(4z+5u)=

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Solution for (9z+-1u)(4z+5u)= equation: 


Simplifying
(9z + -1u)(4z + 5u) = 0

Reorder the terms:
(-1u + 9z)(4z + 5u) = 0

Reorder the terms:
(-1u + 9z)(5u + 4z) = 0

Multiply (-1u + 9z) * (5u + 4z)
(-1u * (5u + 4z) + 9z * (5u + 4z)) = 0
((5u * -1u + 4z * -1u) + 9z * (5u + 4z)) = 0

Reorder the terms:
((-4uz + -5u2) + 9z * (5u + 4z)) = 0
((-4uz + -5u2) + 9z * (5u + 4z)) = 0
(-4uz + -5u2 + (5u * 9z + 4z * 9z)) = 0
(-4uz + -5u2 + (45uz + 36z2)) = 0

Reorder the terms:
(-4uz + 45uz + -5u2 + 36z2) = 0

Combine like terms: -4uz + 45uz = 41uz
(41uz + -5u2 + 36z2) = 0

Solving
41uz + -5u2 + 36z2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-5u + -4z)(u + -9z) = 0


Subproblem 1
Set the factor '(-5u + -4z)' equal to zero and attempt to solve:

Simplifying
-5u + -4z = 0

Solving
-5u + -4z = 0

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

Add '4z' to each side of the equation.
-5u + -4z + 4z = 0 + 4z

Combine like terms: -4z + 4z = 0
-5u + 0 = 0 + 4z
-5u = 0 + 4z
Remove the zero:
-5u = 4z

Divide each side by '-5'.
u = -0.8z

Simplifying
u = -0.8z

Subproblem 2
Set the factor '(u + -9z)' equal to zero and attempt to solve:

Simplifying
u + -9z = 0

Solving
u + -9z = 0

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

Add '9z' to each side of the equation.
u + -9z + 9z = 0 + 9z

Combine like terms: -9z + 9z = 0
u + 0 = 0 + 9z
u = 0 + 9z
Remove the zero:
u = 9z

Simplifying
u = 9z
Solution
u = {-0.8z, 9z}

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