(9z-u)(4z+6u)=

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Solution for (9z-u)(4z+6u)= equation: 


Simplifying
(9z + -1u)(4z + 6u) = 0

Reorder the terms:
(-1u + 9z)(4z + 6u) = 0

Reorder the terms:
(-1u + 9z)(6u + 4z) = 0

Multiply (-1u + 9z) * (6u + 4z)
(-1u * (6u + 4z) + 9z * (6u + 4z)) = 0
((6u * -1u + 4z * -1u) + 9z * (6u + 4z)) = 0

Reorder the terms:
((-4uz + -6u2) + 9z * (6u + 4z)) = 0
((-4uz + -6u2) + 9z * (6u + 4z)) = 0
(-4uz + -6u2 + (6u * 9z + 4z * 9z)) = 0
(-4uz + -6u2 + (54uz + 36z2)) = 0

Reorder the terms:
(-4uz + 54uz + -6u2 + 36z2) = 0

Combine like terms: -4uz + 54uz = 50uz
(50uz + -6u2 + 36z2) = 0

Solving
50uz + -6u2 + 36z2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25uz + -3u2 + 18z2) = 0

Factor a trinomial.
2((-3u + -2z)(u + -9z)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3u + -2z)' equal to zero and attempt to solve:

Simplifying
-3u + -2z = 0

Solving
-3u + -2z = 0

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

Add '2z' to each side of the equation.
-3u + -2z + 2z = 0 + 2z

Combine like terms: -2z + 2z = 0
-3u + 0 = 0 + 2z
-3u = 0 + 2z
Remove the zero:
-3u = 2z

Divide each side by '-3'.
u = -0.6666666667z

Simplifying
u = -0.6666666667z

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 = {-0.6666666667z, 9z}

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