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

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


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

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

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

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

Combine like terms: -6x + -18x = -24x
(18 + -24x + 6x2) = 0

Solving
18 + -24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -4x + x2) = 0

Factor a trinomial.
6((1 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
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
Solution
x = {1, 3}

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