(d+7)(d+2)=-4

Solution for (d+7)(d+2)=-4 equation:

Simplifying
(d + 7)(d + 2) = -4

Reorder the terms:
(7 + d)(d + 2) = -4

Reorder the terms:
(7 + d)(2 + d) = -4

Multiply (7 + d) * (2 + d)
(7(2 + d) + d(2 + d)) = -4
((2 * 7 + d * 7) + d(2 + d)) = -4
((14 + 7d) + d(2 + d)) = -4
(14 + 7d + (2 * d + d * d)) = -4
(14 + 7d + (2d + d2)) = -4

Combine like terms: 7d + 2d = 9d
(14 + 9d + d2) = -4

Solving
14 + 9d + d2 = -4

Solving for variable 'd'.

Reorder the terms:
14 + 4 + 9d + d2 = -4 + 4

Combine like terms: 14 + 4 = 18
18 + 9d + d2 = -4 + 4

Combine like terms: -4 + 4 = 0
18 + 9d + d2 = 0

Factor a trinomial.
(6 + d)(3 + d) = 0

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

Simplifying
6 + d = 0

Solving
6 + d = 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 + d = 0 + -6

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

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

Simplifying
d = -6
Subproblem 2
Set the factor '(3 + d)' equal to zero and attempt to solve:

Simplifying
3 + d = 0

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

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

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

Simplifying
d = -3
Solution
d = {-6, -3}