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

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

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

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

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

Multiply (-1 + 9x) * (9 + 2x)
(-1(9 + 2x) + 9x * (9 + 2x)) = 0
((9 * -1 + 2x * -1) + 9x * (9 + 2x)) = 0
((-9 + -2x) + 9x * (9 + 2x)) = 0
(-9 + -2x + (9 * 9x + 2x * 9x)) = 0
(-9 + -2x + (81x + 18x2)) = 0

Combine like terms: -2x + 81x = 79x
(-9 + 79x + 18x2) = 0

Solving
-9 + 79x + 18x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5
Subproblem 2
Set the factor '(1 + -9x)' equal to zero and attempt to solve:

Simplifying
1 + -9x = 0

Solving
1 + -9x = 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 + -9x = 0 + -1

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

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

Divide each side by '-9'.
x = 0.1111111111

Simplifying
x = 0.1111111111
Solution
x = {-4.5, 0.1111111111}