(d+1)(8d+1)=18d

Solution for (d+1)(8d+1)=18d equation:

Simplifying
(d + 1)(8d + 1) = 18d

Reorder the terms:
(1 + d)(8d + 1) = 18d

Reorder the terms:
(1 + d)(1 + 8d) = 18d

Multiply (1 + d) * (1 + 8d)
(1(1 + 8d) + d(1 + 8d)) = 18d
((1 * 1 + 8d * 1) + d(1 + 8d)) = 18d
((1 + 8d) + d(1 + 8d)) = 18d
(1 + 8d + (1 * d + 8d * d)) = 18d
(1 + 8d + (1d + 8d2)) = 18d

Combine like terms: 8d + 1d = 9d
(1 + 9d + 8d2) = 18d

Solving
1 + 9d + 8d2 = 18d

Solving for variable 'd'.

Reorder the terms:
1 + 9d + -18d + 8d2 = 18d + -18d

Combine like terms: 9d + -18d = -9d
1 + -9d + 8d2 = 18d + -18d

Combine like terms: 18d + -18d = 0
1 + -9d + 8d2 = 0

Factor a trinomial.
(1 + -8d)(1 + -1d) = 0

Subproblem 1
Set the factor '(1 + -8d)' equal to zero and attempt to solve:

Simplifying
1 + -8d = 0

Solving
1 + -8d = 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 + -8d = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8d = 0 + -1
-8d = 0 + -1

Combine like terms: 0 + -1 = -1
-8d = -1

Divide each side by '-8'.
d = 0.125

Simplifying
d = 0.125
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 = {0.125, 1}