(2x-9)(3x-9)=0

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Solution for (2x-9)(3x-9)=0 equation: 


Simplifying
(2x + -9)(3x + -9) = 0

Reorder the terms:
(-9 + 2x)(3x + -9) = 0

Reorder the terms:
(-9 + 2x)(-9 + 3x) = 0

Multiply (-9 + 2x) * (-9 + 3x)
(-9(-9 + 3x) + 2x * (-9 + 3x)) = 0
((-9 * -9 + 3x * -9) + 2x * (-9 + 3x)) = 0
((81 + -27x) + 2x * (-9 + 3x)) = 0
(81 + -27x + (-9 * 2x + 3x * 2x)) = 0
(81 + -27x + (-18x + 6x2)) = 0

Combine like terms: -27x + -18x = -45x
(81 + -45x + 6x2) = 0

Solving
81 + -45x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + -15x + 2x2) = 0

Factor a trinomial.
3((3 + -1x)(9 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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 = {3, 4.5}

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