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

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


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

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

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

Combine like terms: 2x + 12x = 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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