(d+1)(3d+1)=8d

Solution for (d+1)(3d+1)=8d equation:

Simplifying
(d + 1)(3d + 1) = 8d

Reorder the terms:
(1 + d)(3d + 1) = 8d

Reorder the terms:
(1 + d)(1 + 3d) = 8d

Multiply (1 + d) * (1 + 3d)
(1(1 + 3d) + d(1 + 3d)) = 8d
((1 * 1 + 3d * 1) + d(1 + 3d)) = 8d
((1 + 3d) + d(1 + 3d)) = 8d
(1 + 3d + (1 * d + 3d * d)) = 8d
(1 + 3d + (1d + 3d2)) = 8d

Combine like terms: 3d + 1d = 4d
(1 + 4d + 3d2) = 8d

Solving
1 + 4d + 3d2 = 8d

Solving for variable 'd'.

Reorder the terms:
1 + 4d + -8d + 3d2 = 8d + -8d

Combine like terms: 4d + -8d = -4d
1 + -4d + 3d2 = 8d + -8d

Combine like terms: 8d + -8d = 0
1 + -4d + 3d2 = 0

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

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

Simplifying
1 + -3d = 0

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

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

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

Divide each side by '-3'.
d = 0.3333333333

Simplifying
d = 0.3333333333
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 = {0.3333333333, 1}