=16r^2+72rd+81d^2

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Solution for =16r^2+72rd+81d^2 equation: 


Simplifying
0 = 16r2 + 72rd + 81d2

Reorder the terms:
0 = 72dr + 81d2 + 16r2

Solving
0 = 72dr + 81d2 + 16r2

Solving for variable 'd'.
Remove the zero:
-72dr + -81d2 + -16r2 = 72dr + 81d2 + 16r2 + -72dr + -81d2 + -16r2

Reorder the terms:
-72dr + -81d2 + -16r2 = 72dr + -72dr + 81d2 + -81d2 + 16r2 + -16r2

Combine like terms: 72dr + -72dr = 0
-72dr + -81d2 + -16r2 = 0 + 81d2 + -81d2 + 16r2 + -16r2
-72dr + -81d2 + -16r2 = 81d2 + -81d2 + 16r2 + -16r2

Combine like terms: 81d2 + -81d2 = 0
-72dr + -81d2 + -16r2 = 0 + 16r2 + -16r2
-72dr + -81d2 + -16r2 = 16r2 + -16r2

Combine like terms: 16r2 + -16r2 = 0
-72dr + -81d2 + -16r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(72dr + 81d2 + 16r2) = 0

Factor a trinomial.
-1((9d + 4r)(9d + 4r)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9d + 4r)' equal to zero and attempt to solve:

Simplifying
9d + 4r = 0

Solving
9d + 4r = 0

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

Add '-4r' to each side of the equation.
9d + 4r + -4r = 0 + -4r

Combine like terms: 4r + -4r = 0
9d + 0 = 0 + -4r
9d = 0 + -4r
Remove the zero:
9d = -4r

Divide each side by '9'.
d = -0.4444444444r

Simplifying
d = -0.4444444444r

Subproblem 2
Set the factor '(9d + 4r)' equal to zero and attempt to solve:

Simplifying
9d + 4r = 0

Solving
9d + 4r = 0

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

Add '-4r' to each side of the equation.
9d + 4r + -4r = 0 + -4r

Combine like terms: 4r + -4r = 0
9d + 0 = 0 + -4r
9d = 0 + -4r
Remove the zero:
9d = -4r

Divide each side by '9'.
d = -0.4444444444r

Simplifying
d = -0.4444444444r
Solution
d = {-0.4444444444r, -0.4444444444r}

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