b^2+10bd+21d^2=0

Solution for b^2+10bd+21d^2=0 equation:

Simplifying
b2 + 10bd + 21d2 = 0

Reorder the terms:
10bd + b2 + 21d2 = 0

Solving
10bd + b2 + 21d2 = 0

Solving for variable 'b'.

Factor a trinomial.
(b + 3d)(b + 7d) = 0

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

Simplifying
b + 3d = 0

Solving
b + 3d = 0

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

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

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

Simplifying
b = -3d
Subproblem 2
Set the factor '(b + 7d)' equal to zero and attempt to solve:

Simplifying
b + 7d = 0

Solving
b + 7d = 0

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

Add '-7d' to each side of the equation.
b + 7d + -7d = 0 + -7d

Combine like terms: 7d + -7d = 0
b + 0 = 0 + -7d
b = 0 + -7d
Remove the zero:
b = -7d

Simplifying
b = -7d
Solution
b = {-3d, -7d}