(mx+qx)(my+qy)=0

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Solution for (mx+qx)(my+qy)=0 equation: 


Simplifying
(mx + qx)(my + qy) = 0

Multiply (mx + qx) * (my + qy)
(mx(my + qy) + qx(my + qy)) = 0
((my * mx + qy * mx) + qx(my + qy)) = 0

Reorder the terms:
((mqxy + m2xy) + qx(my + qy)) = 0
((mqxy + m2xy) + qx(my + qy)) = 0
(mqxy + m2xy + (my * qx + qy * qx)) = 0
(mqxy + m2xy + (mqxy + q2xy)) = 0

Reorder the terms:
(mqxy + mqxy + m2xy + q2xy) = 0

Combine like terms: mqxy + mqxy = 2mqxy
(2mqxy + m2xy + q2xy) = 0

Solving
2mqxy + m2xy + q2xy = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'xy'.
xy(2mq + m2 + q2) = 0

Factor a trinomial.
xy((m + q)(m + q)) = 0


Subproblem 1
Set the factor 'xy' equal to zero and attempt to solve:

Simplifying
xy = 0

Solving
xy = 0

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

Add '-1xy' to each side of the equation.
xy + -1xy = 0 + -1xy
Remove the zero:
0 = -1xy

Simplifying
0 = -1xy

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
m + q = 0

Solving
m + q = 0

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

Add '-1q' to each side of the equation.
m + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
m + 0 = 0 + -1q
m = 0 + -1q
Remove the zero:
m = -1q

Simplifying
m = -1q

Subproblem 3
Set the factor '(m + q)' equal to zero and attempt to solve:

Simplifying
m + q = 0

Solving
m + q = 0

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

Add '-1q' to each side of the equation.
m + q + -1q = 0 + -1q

Combine like terms: q + -1q = 0
m + 0 = 0 + -1q
m = 0 + -1q
Remove the zero:
m = -1q

Simplifying
m = -1q
Solution
m = {-1q, -1q}

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