(3x-6)(2x-9)=

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Solution for (3x-6)(2x-9)= equation: 


Simplifying
(3x + -6)(2x + -9) = 0

Reorder the terms:
(-6 + 3x)(2x + -9) = 0

Reorder the terms:
(-6 + 3x)(-9 + 2x) = 0

Multiply (-6 + 3x) * (-9 + 2x)
(-6(-9 + 2x) + 3x * (-9 + 2x)) = 0
((-9 * -6 + 2x * -6) + 3x * (-9 + 2x)) = 0
((54 + -12x) + 3x * (-9 + 2x)) = 0
(54 + -12x + (-9 * 3x + 2x * 3x)) = 0
(54 + -12x + (-27x + 6x2)) = 0

Combine like terms: -12x + -27x = -39x
(54 + -39x + 6x2) = 0

Solving
54 + -39x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -13x + 2x2) = 0

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

Ignore the factor 3.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 4.5}

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