-d^2+[9d+(2-4d^2)]=0

Solution for -d^2+[9d+(2-4d^2)]=0 equation:

Simplifying
-1d2 + [9d + (2 + -4d2)] = 0

Remove parenthesis around (2 + -4d2)
-1d2 + [9d + 2 + -4d2] = 0

Reorder the terms:
-1d2 + [2 + 9d + -4d2] = 0

Remove brackets around [2 + 9d + -4d2]
-1d2 + 2 + 9d + -4d2 = 0

Reorder the terms:
2 + 9d + -1d2 + -4d2 = 0

Combine like terms: -1d2 + -4d2 = -5d2
2 + 9d + -5d2 = 0

Solving
2 + 9d + -5d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(2 + -1d)(1 + 5d) = 0

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

Simplifying
2 + -1d = 0

Solving
2 + -1d = 0

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

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

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

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

Divide each side by '-1'.
d = 2

Simplifying
d = 2
Subproblem 2
Set the factor '(1 + 5d)' equal to zero and attempt to solve:

Simplifying
1 + 5d = 0

Solving
1 + 5d = 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 + 5d = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5d = 0 + -1
5d = 0 + -1

Combine like terms: 0 + -1 = -1
5d = -1

Divide each side by '5'.
d = -0.2

Simplifying
d = -0.2
Solution
d = {2, -0.2}