6d^2-5d-21=0

Solution for 6d^2-5d-21=0 equation:

Simplifying
6d2 + -5d + -21 = 0

Reorder the terms:
-21 + -5d + 6d2 = 0

Solving
-21 + -5d + 6d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-3 + -2d)(7 + -3d) = 0

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

Simplifying
-3 + -2d = 0

Solving
-3 + -2d = 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 + -2d = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2d = 0 + 3
-2d = 0 + 3

Combine like terms: 0 + 3 = 3
-2d = 3

Divide each side by '-2'.
d = -1.5

Simplifying
d = -1.5
Subproblem 2
Set the factor '(7 + -3d)' equal to zero and attempt to solve:

Simplifying
7 + -3d = 0

Solving
7 + -3d = 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 + -3d = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3d = 0 + -7
-3d = 0 + -7

Combine like terms: 0 + -7 = -7
-3d = -7

Divide each side by '-3'.
d = 2.333333333

Simplifying
d = 2.333333333
Solution
d = {-1.5, 2.333333333}