(6a-9uv)(a+uv)=

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Solution for (6a-9uv)(a+uv)= equation: 


Simplifying
(6a + -9uv)(a + uv) = 0

Multiply (6a + -9uv) * (a + uv)
(6a * (a + uv) + -9uv * (a + uv)) = 0
((a * 6a + uv * 6a) + -9uv * (a + uv)) = 0

Reorder the terms:
((6auv + 6a2) + -9uv * (a + uv)) = 0
((6auv + 6a2) + -9uv * (a + uv)) = 0
(6auv + 6a2 + (a * -9uv + uv * -9uv)) = 0
(6auv + 6a2 + (-9auv + -9u2v2)) = 0

Reorder the terms:
(6auv + -9auv + 6a2 + -9u2v2) = 0

Combine like terms: 6auv + -9auv = -3auv
(-3auv + 6a2 + -9u2v2) = 0

Solving
-3auv + 6a2 + -9u2v2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1auv + 2a2 + -3u2v2) = 0

Factor a trinomial.
3((2a + -3uv)(a + uv)) = 0

Ignore the factor 3.

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

Simplifying
2a + -3uv = 0

Solving
2a + -3uv = 0

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

Add '3uv' to each side of the equation.
2a + -3uv + 3uv = 0 + 3uv

Combine like terms: -3uv + 3uv = 0
2a + 0 = 0 + 3uv
2a = 0 + 3uv
Remove the zero:
2a = 3uv

Divide each side by '2'.
a = 1.5uv

Simplifying
a = 1.5uv

Subproblem 2
Set the factor '(a + uv)' equal to zero and attempt to solve:

Simplifying
a + uv = 0

Solving
a + uv = 0

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

Add '-1uv' to each side of the equation.
a + uv + -1uv = 0 + -1uv

Combine like terms: uv + -1uv = 0
a + 0 = 0 + -1uv
a = 0 + -1uv
Remove the zero:
a = -1uv

Simplifying
a = -1uv
Solution
a = {1.5uv, -1uv}

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