(3d+5)(d+3)=7

Solution for (3d+5)(d+3)=7 equation:

Simplifying
(3d + 5)(d + 3) = 7

Reorder the terms:
(5 + 3d)(d + 3) = 7

Reorder the terms:
(5 + 3d)(3 + d) = 7

Multiply (5 + 3d) * (3 + d)
(5(3 + d) + 3d * (3 + d)) = 7
((3 * 5 + d * 5) + 3d * (3 + d)) = 7
((15 + 5d) + 3d * (3 + d)) = 7
(15 + 5d + (3 * 3d + d * 3d)) = 7
(15 + 5d + (9d + 3d2)) = 7

Combine like terms: 5d + 9d = 14d
(15 + 14d + 3d2) = 7

Solving
15 + 14d + 3d2 = 7

Solving for variable 'd'.

Reorder the terms:
15 + -7 + 14d + 3d2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14d + 3d2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14d + 3d2 = 0

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

Subproblem 1
Set the factor '(4 + d)' equal to zero and attempt to solve:

Simplifying
4 + d = 0

Solving
4 + d = 0

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

Add '-4' to each side of the equation.
4 + -4 + d = 0 + -4

Combine like terms: 4 + -4 = 0
0 + d = 0 + -4
d = 0 + -4

Combine like terms: 0 + -4 = -4
d = -4

Simplifying
d = -4
Subproblem 2
Set the factor '(2 + 3d)' equal to zero and attempt to solve:

Simplifying
2 + 3d = 0

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

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

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

Divide each side by '3'.
d = -0.6666666667

Simplifying
d = -0.6666666667
Solution
d = {-4, -0.6666666667}