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

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

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

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

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

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

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

Solving
8 + -9x + x2 = 18

Solving for variable 'x'.

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

Combine like terms: 8 + -18 = -10
-10 + -9x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-10 + -9x + x2 = 0

Factor a trinomial.
(-1 + -1x)(10 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-1, 10}