4d+2=(d-1)(d+3)

Solution for 4d+2=(d-1)(d+3) equation:

Simplifying
4d + 2 = (d + -1)(d + 3)

Reorder the terms:
2 + 4d = (d + -1)(d + 3)

Reorder the terms:
2 + 4d = (-1 + d)(d + 3)

Reorder the terms:
2 + 4d = (-1 + d)(3 + d)

Multiply (-1 + d) * (3 + d)
2 + 4d = (-1(3 + d) + d(3 + d))
2 + 4d = ((3 * -1 + d * -1) + d(3 + d))
2 + 4d = ((-3 + -1d) + d(3 + d))
2 + 4d = (-3 + -1d + (3 * d + d * d))
2 + 4d = (-3 + -1d + (3d + d2))

Combine like terms: -1d + 3d = 2d
2 + 4d = (-3 + 2d + d2)

Solving
2 + 4d = -3 + 2d + d2

Solving for variable 'd'.

Reorder the terms:
2 + 3 + 4d + -2d + -1d2 = -3 + 2d + d2 + 3 + -2d + -1d2

Combine like terms: 2 + 3 = 5
5 + 4d + -2d + -1d2 = -3 + 2d + d2 + 3 + -2d + -1d2

Combine like terms: 4d + -2d = 2d
5 + 2d + -1d2 = -3 + 2d + d2 + 3 + -2d + -1d2

Reorder the terms:
5 + 2d + -1d2 = -3 + 3 + 2d + -2d + d2 + -1d2

Combine like terms: -3 + 3 = 0
5 + 2d + -1d2 = 0 + 2d + -2d + d2 + -1d2
5 + 2d + -1d2 = 2d + -2d + d2 + -1d2

Combine like terms: 2d + -2d = 0
5 + 2d + -1d2 = 0 + d2 + -1d2
5 + 2d + -1d2 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
5 + 2d + -1d2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-5 + -2d + d2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2d + 5 + d2 = 0 + 5

Reorder the terms:
-5 + 5 + -2d + d2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2d + d2 = 0 + 5
-2d + d2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2d + d2 = 5

The d term is -2d.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2d + 1 + d2 = 5 + 1

Reorder the terms:
1 + -2d + d2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2d + d2 = 6

Factor a perfect square on the left side:
(d + -1)(d + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(d + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
d + -1 = 2.449489743

Simplifying
d + -1 = 2.449489743

Reorder the terms:
-1 + d = 2.449489743

Solving
-1 + d = 2.449489743

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + d = 2.449489743 + 1
d = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
d = 3.449489743

Simplifying
d = 3.449489743

Subproblem 2
d + -1 = -2.449489743

Simplifying
d + -1 = -2.449489743

Reorder the terms:
-1 + d = -2.449489743

Solving
-1 + d = -2.449489743

Solving for variable 'd'.

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

Add '1' to each side of the equation.
-1 + 1 + d = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + d = -2.449489743 + 1
d = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
d = -1.449489743

Simplifying
d = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {3.449489743, -1.449489743}