(3d-1)(d+2)=0

Solution for (3d-1)(d+2)=0 equation:

Simplifying
(3d + -1)(d + 2) = 0

Reorder the terms:
(-1 + 3d)(d + 2) = 0

Reorder the terms:
(-1 + 3d)(2 + d) = 0

Multiply (-1 + 3d) * (2 + d)
(-1(2 + d) + 3d * (2 + d)) = 0
((2 * -1 + d * -1) + 3d * (2 + d)) = 0
((-2 + -1d) + 3d * (2 + d)) = 0
(-2 + -1d + (2 * 3d + d * 3d)) = 0
(-2 + -1d + (6d + 3d2)) = 0

Combine like terms: -1d + 6d = 5d
(-2 + 5d + 3d2) = 0

Solving
-2 + 5d + 3d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-2 + -1d)(1 + -3d) = 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 + -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 = {-2, 0.3333333333}