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

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

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

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

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

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

Solving for variable 'x'.

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

Reorder the terms:
-6 + 9x + -3x2 = -6x + 6x + 3x2 + -3x2

Combine like terms: -6x + 6x = 0
-6 + 9x + -3x2 = 0 + 3x2 + -3x2
-6 + 9x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6 + 9x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3x + -1x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, 1}