6b^2+17bd+12d^2=0

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Solution for 6b^2+17bd+12d^2=0 equation: 


Simplifying
6b2 + 17bd + 12d2 = 0

Reorder the terms:
17bd + 6b2 + 12d2 = 0

Solving
17bd + 6b2 + 12d2 = 0

Solving for variable 'b'.

Factor a trinomial.
(3b + 4d)(2b + 3d) = 0


Subproblem 1
Set the factor '(3b + 4d)' equal to zero and attempt to solve:

Simplifying
3b + 4d = 0

Solving
3b + 4d = 0

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

Add '-4d' to each side of the equation.
3b + 4d + -4d = 0 + -4d

Combine like terms: 4d + -4d = 0
3b + 0 = 0 + -4d
3b = 0 + -4d
Remove the zero:
3b = -4d

Divide each side by '3'.
b = -1.333333333d

Simplifying
b = -1.333333333d

Subproblem 2
Set the factor '(2b + 3d)' equal to zero and attempt to solve:

Simplifying
2b + 3d = 0

Solving
2b + 3d = 0

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

Add '-3d' to each side of the equation.
2b + 3d + -3d = 0 + -3d

Combine like terms: 3d + -3d = 0
2b + 0 = 0 + -3d
2b = 0 + -3d
Remove the zero:
2b = -3d

Divide each side by '2'.
b = -1.5d

Simplifying
b = -1.5d
Solution
b = {-1.333333333d, -1.5d}

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