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

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


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

Reorder the terms:
3x(-4 + 2x) = 6(x + -2)
(-4 * 3x + 2x * 3x) = 6(x + -2)
(-12x + 6x2) = 6(x + -2)

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
6((1 + -1x)(2 + -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 '(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 = {1, 2}

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