(3d+1)(5-2d)=

Solution for (3d+1)(5-2d)= equation:

Simplifying
(3d + 1)(5 + -2d) = 0

Reorder the terms:
(1 + 3d)(5 + -2d) = 0

Multiply (1 + 3d) * (5 + -2d)
(1(5 + -2d) + 3d * (5 + -2d)) = 0
((5 * 1 + -2d * 1) + 3d * (5 + -2d)) = 0
((5 + -2d) + 3d * (5 + -2d)) = 0
(5 + -2d + (5 * 3d + -2d * 3d)) = 0
(5 + -2d + (15d + -6d2)) = 0

Combine like terms: -2d + 15d = 13d
(5 + 13d + -6d2) = 0

Solving
5 + 13d + -6d2 = 0

Solving for variable 'd'.

Factor a trinomial.
(5 + -2d)(1 + 3d) = 0

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

Simplifying
5 + -2d = 0

Solving
5 + -2d = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2d = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2d = 0 + -5
-2d = 0 + -5

Combine like terms: 0 + -5 = -5
-2d = -5

Divide each side by '-2'.
d = 2.5

Simplifying
d = 2.5
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 = {2.5, -0.3333333333}