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

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

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

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

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

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

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

Reorder the terms:
-3 + 3 + 2d + d2 = 0

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

Solving
2d + d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), 'd'.
d(2 + d) = 0

Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0
Subproblem 2
Set the factor '(2 + d)' equal to zero and attempt to solve:

Simplifying
2 + d = 0

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

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

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

Simplifying
d = -2
Solution
d = {0, -2}