2d^2+3d-54=0

Solution for 2d^2+3d-54=0 equation:

Simplifying
2d2 + 3d + -54 = 0

Reorder the terms:
-54 + 3d + 2d2 = 0

Solving
-54 + 3d + 2d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-6 + -1d)(9 + -2d) = 0

Subproblem 1
Set the factor '(-6 + -1d)' equal to zero and attempt to solve:

Simplifying
-6 + -1d = 0

Solving
-6 + -1d = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1d = 0 + 6

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

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

Divide each side by '-1'.
d = -6

Simplifying
d = -6
Subproblem 2
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
Solution
d = {-6, 4.5}