4d^2+1+4d=0

Solution for 4d^2+1+4d=0 equation:

Simplifying
4d2 + 1 + 4d = 0

Reorder the terms:
1 + 4d + 4d2 = 0

Solving
1 + 4d + 4d2 = 0

Solving for variable 'd'.

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

Subproblem 1
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
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 = {-0.5, -0.5}