(2x-5)(9x+2)=0

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Solution for (2x-5)(9x+2)=0 equation: 


Simplifying
(2x + -5)(9x + 2) = 0

Reorder the terms:
(-5 + 2x)(9x + 2) = 0

Reorder the terms:
(-5 + 2x)(2 + 9x) = 0

Multiply (-5 + 2x) * (2 + 9x)
(-5(2 + 9x) + 2x * (2 + 9x)) = 0
((2 * -5 + 9x * -5) + 2x * (2 + 9x)) = 0
((-10 + -45x) + 2x * (2 + 9x)) = 0
(-10 + -45x + (2 * 2x + 9x * 2x)) = 0
(-10 + -45x + (4x + 18x2)) = 0

Combine like terms: -45x + 4x = -41x
(-10 + -41x + 18x2) = 0

Solving
-10 + -41x + 18x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -9x)(5 + -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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.2222222222, 2.5}

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