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

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


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

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

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

Multiply (9 + 2x) * (-2 + 9x)
(9(-2 + 9x) + 2x * (-2 + 9x)) = 0
((-2 * 9 + 9x * 9) + 2x * (-2 + 9x)) = 0
((-18 + 81x) + 2x * (-2 + 9x)) = 0
(-18 + 81x + (-2 * 2x + 9x * 2x)) = 0
(-18 + 81x + (-4x + 18x2)) = 0

Combine like terms: 81x + -4x = 77x
(-18 + 77x + 18x2) = 0

Solving
-18 + 77x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(2 + -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 '(2 + -9x)' equal to zero and attempt to solve:

Simplifying
2 + -9x = 0

Solving
2 + -9x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -9x = 0 + -2

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

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

Divide each side by '-9'.
x = 0.2222222222

Simplifying
x = 0.2222222222
Solution
x = {-4.5, 0.2222222222}

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