6d-1=9d^2

Solution for 6d-1=9d^2 equation:

Simplifying
6d + -1 = 9d2

Reorder the terms:
-1 + 6d = 9d2

Solving
-1 + 6d = 9d2

Solving for variable 'd'.

Combine like terms: 9d2 + -9d2 = 0
-1 + 6d + -9d2 = 0

Factor a trinomial.
(-1 + 3d)(1 + -3d) = 0

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

Simplifying
-1 + 3d = 0

Solving
-1 + 3d = 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 + 3d = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3d = 0 + 1
3d = 0 + 1

Combine like terms: 0 + 1 = 1
3d = 1

Divide each side by '3'.
d = 0.3333333333

Simplifying
d = 0.3333333333
Subproblem 2
Set the factor '(1 + -3d)' equal to zero and attempt to solve:

Simplifying
1 + -3d = 0

Solving
1 + -3d = 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 + -3d = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3d = 0 + -1
-3d = 0 + -1

Combine like terms: 0 + -1 = -1
-3d = -1

Divide each side by '-3'.
d = 0.3333333333

Simplifying
d = 0.3333333333
Solution
d = {0.3333333333, 0.3333333333}