r^2d^2+10rd+21=0

Solution for r^2d^2+10rd+21=0 equation:

Simplifying
r2d2 + 10rd + 21 = 0

Reorder the terms:
21 + 10dr + d2r2 = 0

Solving
21 + 10dr + d2r2 = 0

Solving for variable 'd'.

Factor a trinomial.
(7 + dr)(3 + dr) = 0

Subproblem 1
Set the factor '(7 + dr)' equal to zero and attempt to solve:

Simplifying
7 + dr = 0

Solving
7 + dr = 0

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

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

Combine like terms: 7 + -7 = 0
0 + dr = 0 + -7
dr = 0 + -7

Combine like terms: 0 + -7 = -7
dr = -7

Divide each side by 'r'.
d = -7r-1

Simplifying
d = -7r-1
Subproblem 2
Set the factor '(3 + dr)' equal to zero and attempt to solve:

Simplifying
3 + dr = 0

Solving
3 + dr = 0

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

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

Combine like terms: 3 + -3 = 0
0 + dr = 0 + -3
dr = 0 + -3

Combine like terms: 0 + -3 = -3
dr = -3

Divide each side by 'r'.
d = -3r-1

Simplifying
d = -3r-1
Solution
d = {-7r-1, -3r-1}