(dx+dy)(6dx+dy)=0

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Solution for (dx+dy)(6dx+dy)=0 equation: 


Simplifying
(dx + dy)(6dx + dy) = 0

Multiply (dx + dy) * (6dx + dy)
(dx(6dx + dy) + dy(6dx + dy)) = 0
((6dx * dx + dy * dx) + dy(6dx + dy)) = 0

Reorder the terms:
((d2xy + 6d2x2) + dy(6dx + dy)) = 0
((d2xy + 6d2x2) + dy(6dx + dy)) = 0
(d2xy + 6d2x2 + (6dx * dy + dy * dy)) = 0
(d2xy + 6d2x2 + (6d2xy + d2y2)) = 0

Reorder the terms:
(d2xy + 6d2xy + 6d2x2 + d2y2) = 0

Combine like terms: d2xy + 6d2xy = 7d2xy
(7d2xy + 6d2x2 + d2y2) = 0

Solving
7d2xy + 6d2x2 + d2y2 = 0

Solving for variable 'd'.

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

Factor out the Greatest Common Factor (GCF), 'd2'.
d2(7xy + 6x2 + y2) = 0

Factor a trinomial.
d2((6x + y)(x + y)) = 0


Subproblem 1
Set the factor 'd2' equal to zero and attempt to solve:

Simplifying
d2 = 0

Solving
d2 = 0

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

Simplifying
d2 = 0

Take the square root of each side:
d = {0}

Subproblem 2
Set the factor '(6x + y)' equal to zero and attempt to solve:

Simplifying
6x + y = 0

Solving
6x + y = 0

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

Add '-6x' to each side of the equation.
6x + -6x + y = 0 + -6x

Combine like terms: 6x + -6x = 0
0 + y = 0 + -6x
y = 0 + -6x
Remove the zero:
y = -6x

Add '-1y' to each side of the equation.
y + -1y = -6x + -1y

Combine like terms: y + -1y = 0
0 = -6x + -1y

Simplifying
0 = -6x + -1y

The solution to this equation could not be determined.

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

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

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1x' to each side of the equation.
x + -1x + y = 0 + -1x

Combine like terms: x + -1x = 0
0 + y = 0 + -1x
y = 0 + -1x
Remove the zero:
y = -1x

Add '-1y' to each side of the equation.
y + -1y = -1x + -1y

Combine like terms: y + -1y = 0
0 = -1x + -1y

Simplifying
0 = -1x + -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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