(2d+3)(d+1)-3(d+2)(d+1)=-3(d+5)

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Solution for (2d+3)(d+1)-3(d+2)(d+1)=-3(d+5) equation: 


Simplifying
(2d + 3)(d + 1) + -3(d + 2)(d + 1) = -3(d + 5)

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

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

Multiply (3 + 2d) * (1 + d)
(3(1 + d) + 2d * (1 + d)) + -3(d + 2)(d + 1) = -3(d + 5)
((1 * 3 + d * 3) + 2d * (1 + d)) + -3(d + 2)(d + 1) = -3(d + 5)
((3 + 3d) + 2d * (1 + d)) + -3(d + 2)(d + 1) = -3(d + 5)
(3 + 3d + (1 * 2d + d * 2d)) + -3(d + 2)(d + 1) = -3(d + 5)
(3 + 3d + (2d + 2d2)) + -3(d + 2)(d + 1) = -3(d + 5)

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

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

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

Multiply (2 + d) * (1 + d)
3 + 5d + 2d2 + -3(2(1 + d) + d(1 + d)) = -3(d + 5)
3 + 5d + 2d2 + -3((1 * 2 + d * 2) + d(1 + d)) = -3(d + 5)
3 + 5d + 2d2 + -3((2 + 2d) + d(1 + d)) = -3(d + 5)
3 + 5d + 2d2 + -3(2 + 2d + (1 * d + d * d)) = -3(d + 5)
3 + 5d + 2d2 + -3(2 + 2d + (1d + d2)) = -3(d + 5)

Combine like terms: 2d + 1d = 3d
3 + 5d + 2d2 + -3(2 + 3d + d2) = -3(d + 5)
3 + 5d + 2d2 + (2 * -3 + 3d * -3 + d2 * -3) = -3(d + 5)
3 + 5d + 2d2 + (-6 + -9d + -3d2) = -3(d + 5)

Reorder the terms:
3 + -6 + 5d + -9d + 2d2 + -3d2 = -3(d + 5)

Combine like terms: 3 + -6 = -3
-3 + 5d + -9d + 2d2 + -3d2 = -3(d + 5)

Combine like terms: 5d + -9d = -4d
-3 + -4d + 2d2 + -3d2 = -3(d + 5)

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

Reorder the terms:
-3 + -4d + -1d2 = -3(5 + d)
-3 + -4d + -1d2 = (5 * -3 + d * -3)
-3 + -4d + -1d2 = (-15 + -3d)

Solving
-3 + -4d + -1d2 = -15 + -3d

Solving for variable 'd'.

Reorder the terms:
-3 + 15 + -4d + 3d + -1d2 = -15 + -3d + 15 + 3d

Combine like terms: -3 + 15 = 12
12 + -4d + 3d + -1d2 = -15 + -3d + 15 + 3d

Combine like terms: -4d + 3d = -1d
12 + -1d + -1d2 = -15 + -3d + 15 + 3d

Reorder the terms:
12 + -1d + -1d2 = -15 + 15 + -3d + 3d

Combine like terms: -15 + 15 = 0
12 + -1d + -1d2 = 0 + -3d + 3d
12 + -1d + -1d2 = -3d + 3d

Combine like terms: -3d + 3d = 0
12 + -1d + -1d2 = 0

Factor a trinomial.
(3 + -1d)(4 + d) = 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 '(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
Solution
d = {3, -4}

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