(x+1)(8x+1)-18x=0

Solution for (x+1)(8x+1)-18x=0 equation:

Simplifying
(x + 1)(8x + 1) + -18x = 0

Reorder the terms:
(1 + x)(8x + 1) + -18x = 0

Reorder the terms:
(1 + x)(1 + 8x) + -18x = 0

Multiply (1 + x) * (1 + 8x)
(1(1 + 8x) + x(1 + 8x)) + -18x = 0
((1 * 1 + 8x * 1) + x(1 + 8x)) + -18x = 0
((1 + 8x) + x(1 + 8x)) + -18x = 0
(1 + 8x + (1 * x + 8x * x)) + -18x = 0
(1 + 8x + (1x + 8x2)) + -18x = 0

Combine like terms: 8x + 1x = 9x
(1 + 9x + 8x2) + -18x = 0

Reorder the terms:
1 + 9x + -18x + 8x2 = 0

Combine like terms: 9x + -18x = -9x
1 + -9x + 8x2 = 0

Solving
1 + -9x + 8x2 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + -8x = 0

Solving
1 + -8x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8x = 0 + -1

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

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

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

Simplifying
x = 0.125
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0.125, 1}