4d^2+20d+9=0

Solution for 4d^2+20d+9=0 equation:

Simplifying
4d2 + 20d + 9 = 0

Reorder the terms:
9 + 20d + 4d2 = 0

Solving
9 + 20d + 4d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(9 + 2d)(1 + 2d) = 0

Subproblem 1
Set the factor '(9 + 2d)' equal to zero and attempt to solve:

Simplifying
9 + 2d = 0

Solving
9 + 2d = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2d = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2d = 0 + -9
2d = 0 + -9

Combine like terms: 0 + -9 = -9
2d = -9

Divide each side by '2'.
d = -4.5

Simplifying
d = -4.5
Subproblem 2
Set the factor '(1 + 2d)' equal to zero and attempt to solve:

Simplifying
1 + 2d = 0

Solving
1 + 2d = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2d = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2d = 0 + -1
2d = 0 + -1

Combine like terms: 0 + -1 = -1
2d = -1

Divide each side by '2'.
d = -0.5

Simplifying
d = -0.5
Solution
d = {-4.5, -0.5}