(d-3)(d+5)=-12

Solution for (d-3)(d+5)=-12 equation:

Simplifying
(d + -3)(d + 5) = -12

Reorder the terms:
(-3 + d)(d + 5) = -12

Reorder the terms:
(-3 + d)(5 + d) = -12

Multiply (-3 + d) * (5 + d)
(-3(5 + d) + d(5 + d)) = -12
((5 * -3 + d * -3) + d(5 + d)) = -12
((-15 + -3d) + d(5 + d)) = -12
(-15 + -3d + (5 * d + d * d)) = -12
(-15 + -3d + (5d + d2)) = -12

Combine like terms: -3d + 5d = 2d
(-15 + 2d + d2) = -12

Solving
-15 + 2d + d2 = -12

Solving for variable 'd'.

Reorder the terms:
-15 + 12 + 2d + d2 = -12 + 12

Combine like terms: -15 + 12 = -3
-3 + 2d + d2 = -12 + 12

Combine like terms: -12 + 12 = 0
-3 + 2d + d2 = 0

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

Subproblem 1
Set the factor '(-3 + -1d)' equal to zero and attempt to solve:

Simplifying
-3 + -1d = 0

Solving
-3 + -1d = 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 + -1d = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1d = 0 + 3
-1d = 0 + 3

Combine like terms: 0 + 3 = 3
-1d = 3

Divide each side by '-1'.
d = -3

Simplifying
d = -3
Subproblem 2
Set the factor '(1 + -1d)' equal to zero and attempt to solve:

Simplifying
1 + -1d = 0

Solving
1 + -1d = 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 + -1d = 0 + -1

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

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

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

Simplifying
d = 1
Solution
d = {-3, 1}