(x-9)(2x-1)=0

Solution for (x-9)(2x-1)=0 equation:

Simplifying
(x + -9)(2x + -1) = 0

Reorder the terms:
(-9 + x)(2x + -1) = 0

Reorder the terms:
(-9 + x)(-1 + 2x) = 0

Multiply (-9 + x) * (-1 + 2x)
(-9(-1 + 2x) + x(-1 + 2x)) = 0
((-1 * -9 + 2x * -9) + x(-1 + 2x)) = 0
((9 + -18x) + x(-1 + 2x)) = 0
(9 + -18x + (-1 * x + 2x * x)) = 0
(9 + -18x + (-1x + 2x2)) = 0

Combine like terms: -18x + -1x = -19x
(9 + -19x + 2x2) = 0

Solving
9 + -19x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(9 + -1x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0.5, 9}