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

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


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

Reorder the terms:
9(-2 + x) = 3x(x + -2)
(-2 * 9 + x * 9) = 3x(x + -2)
(-18 + 9x) = 3x(x + -2)

Reorder the terms:
-18 + 9x = 3x(-2 + x)
-18 + 9x = (-2 * 3x + x * 3x)
-18 + 9x = (-6x + 3x2)

Solving
-18 + 9x = -6x + 3x2

Solving for variable 'x'.

Combine like terms: 9x + 6x = 15x
-18 + 15x + -3x2 = -6x + 3x2 + 6x + -3x2

Reorder the terms:
-18 + 15x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
-18 + 15x + -3x2 = 0 + 3x2 + -3x2
-18 + 15x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-18 + 15x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 5x + -1x2) = 0

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

Ignore the factor 3.

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

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

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

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

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, 2}

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