(16y-5xd)(15y-11xd)=0

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Solution for (16y-5xd)(15y-11xd)=0 equation: 


Simplifying
(16y + -5xd)(15y + -11xd) = 0

Reorder the terms:
(-5dx + 16y)(15y + -11xd) = 0

Reorder the terms:
(-5dx + 16y)(-11dx + 15y) = 0

Multiply (-5dx + 16y) * (-11dx + 15y)
(-5dx * (-11dx + 15y) + 16y * (-11dx + 15y)) = 0
((-11dx * -5dx + 15y * -5dx) + 16y * (-11dx + 15y)) = 0

Reorder the terms:
((-75dxy + 55d2x2) + 16y * (-11dx + 15y)) = 0
((-75dxy + 55d2x2) + 16y * (-11dx + 15y)) = 0
(-75dxy + 55d2x2 + (-11dx * 16y + 15y * 16y)) = 0
(-75dxy + 55d2x2 + (-176dxy + 240y2)) = 0

Reorder the terms:
(-75dxy + -176dxy + 55d2x2 + 240y2) = 0

Combine like terms: -75dxy + -176dxy = -251dxy
(-251dxy + 55d2x2 + 240y2) = 0

Solving
-251dxy + 55d2x2 + 240y2 = 0

Solving for variable 'd'.

Factor a trinomial.
(5dx + -16y)(11dx + -15y) = 0


Subproblem 1
Set the factor '(5dx + -16y)' equal to zero and attempt to solve:

Simplifying
5dx + -16y = 0

Solving
5dx + -16y = 0

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

Add '16y' to each side of the equation.
5dx + -16y + 16y = 0 + 16y

Combine like terms: -16y + 16y = 0
5dx + 0 = 0 + 16y
5dx = 0 + 16y
Remove the zero:
5dx = 16y

Divide each side by '5x'.
d = 3.2x-1y

Simplifying
d = 3.2x-1y

Subproblem 2
Set the factor '(11dx + -15y)' equal to zero and attempt to solve:

Simplifying
11dx + -15y = 0

Solving
11dx + -15y = 0

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

Add '15y' to each side of the equation.
11dx + -15y + 15y = 0 + 15y

Combine like terms: -15y + 15y = 0
11dx + 0 = 0 + 15y
11dx = 0 + 15y
Remove the zero:
11dx = 15y

Divide each side by '11x'.
d = 1.363636364x-1y

Simplifying
d = 1.363636364x-1y
Solution
d = {3.2x-1y, 1.363636364x-1y}

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