(2x-4)(1-3x)=0

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Solution for (2x-4)(1-3x)=0 equation: 


Simplifying
(2x + -4)(1 + -3x) = 0

Reorder the terms:
(-4 + 2x)(1 + -3x) = 0

Multiply (-4 + 2x) * (1 + -3x)
(-4(1 + -3x) + 2x * (1 + -3x)) = 0
((1 * -4 + -3x * -4) + 2x * (1 + -3x)) = 0
((-4 + 12x) + 2x * (1 + -3x)) = 0
(-4 + 12x + (1 * 2x + -3x * 2x)) = 0
(-4 + 12x + (2x + -6x2)) = 0

Combine like terms: 12x + 2x = 14x
(-4 + 14x + -6x2) = 0

Solving
-4 + 14x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 7x + -3x2) = 0

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

Ignore the factor 2.

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 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {2, 0.3333333333}

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