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

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


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

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

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

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

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

Solving
-18 + -77x + 18x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.2222222222, 4.5}

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