(4a-xy)(2a+2xy)=0

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Solution for (4a-xy)(2a+2xy)=0 equation: 


Simplifying
(4a + -1xy)(2a + 2xy) = 0

Multiply (4a + -1xy) * (2a + 2xy)
(4a * (2a + 2xy) + -1xy * (2a + 2xy)) = 0
((2a * 4a + 2xy * 4a) + -1xy * (2a + 2xy)) = 0

Reorder the terms:
((8axy + 8a2) + -1xy * (2a + 2xy)) = 0
((8axy + 8a2) + -1xy * (2a + 2xy)) = 0
(8axy + 8a2 + (2a * -1xy + 2xy * -1xy)) = 0
(8axy + 8a2 + (-2axy + -2x2y2)) = 0

Reorder the terms:
(8axy + -2axy + 8a2 + -2x2y2) = 0

Combine like terms: 8axy + -2axy = 6axy
(6axy + 8a2 + -2x2y2) = 0

Solving
6axy + 8a2 + -2x2y2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3axy + 4a2 + -1x2y2) = 0

Factor a trinomial.
2((4a + -1xy)(a + xy)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4a + -1xy)' equal to zero and attempt to solve:

Simplifying
4a + -1xy = 0

Solving
4a + -1xy = 0

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

Add 'xy' to each side of the equation.
4a + -1xy + xy = 0 + xy

Combine like terms: -1xy + xy = 0
4a + 0 = 0 + xy
4a = 0 + xy
Remove the zero:
4a = xy

Divide each side by '4'.
a = 0.25xy

Simplifying
a = 0.25xy

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

Simplifying
a + xy = 0

Solving
a + xy = 0

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

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

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

Simplifying
a = -1xy
Solution
a = {0.25xy, -1xy}

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