3(4x-8)=12x(x-2)

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Solution for 3(4x-8)=12x(x-2) equation: 


Simplifying
3(4x + -8) = 12x(x + -2)

Reorder the terms:
3(-8 + 4x) = 12x(x + -2)
(-8 * 3 + 4x * 3) = 12x(x + -2)
(-24 + 12x) = 12x(x + -2)

Reorder the terms:
-24 + 12x = 12x(-2 + x)
-24 + 12x = (-2 * 12x + x * 12x)
-24 + 12x = (-24x + 12x2)

Solving
-24 + 12x = -24x + 12x2

Solving for variable 'x'.

Combine like terms: 12x + 24x = 36x
-24 + 36x + -12x2 = -24x + 12x2 + 24x + -12x2

Reorder the terms:
-24 + 36x + -12x2 = -24x + 24x + 12x2 + -12x2

Combine like terms: -24x + 24x = 0
-24 + 36x + -12x2 = 0 + 12x2 + -12x2
-24 + 36x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-24 + 36x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-2 + 3x + -1x2) = 0

Factor a trinomial.
12((-2 + x)(1 + -1x)) = 0

Ignore the factor 12.

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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