3(2x-4)=6x(x-2)

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Solution for 3(2x-4)=6x(x-2) equation: 


Simplifying
3(2x + -4) = 6x(x + -2)

Reorder the terms:
3(-4 + 2x) = 6x(x + -2)
(-4 * 3 + 2x * 3) = 6x(x + -2)
(-12 + 6x) = 6x(x + -2)

Reorder the terms:
-12 + 6x = 6x(-2 + x)
-12 + 6x = (-2 * 6x + x * 6x)
-12 + 6x = (-12x + 6x2)

Solving
-12 + 6x = -12x + 6x2

Solving for variable 'x'.

Combine like terms: 6x + 12x = 18x
-12 + 18x + -6x2 = -12x + 6x2 + 12x + -6x2

Reorder the terms:
-12 + 18x + -6x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
-12 + 18x + -6x2 = 0 + 6x2 + -6x2
-12 + 18x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-12 + 18x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 3x + -1x2) = 0

Factor a trinomial.
6((-2 + x)(1 + -1x)) = 0

Ignore the factor 6.

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}

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