(3x-1)(4-x)=6

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Solution for (3x-1)(4-x)=6 equation: 


Simplifying
(3x + -1)(4 + -1x) = 6

Reorder the terms:
(-1 + 3x)(4 + -1x) = 6

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

Combine like terms: 1x + 12x = 13x
(-4 + 13x + -3x2) = 6

Solving
-4 + 13x + -3x2 = 6

Solving for variable 'x'.

Reorder the terms:
-4 + -6 + 13x + -3x2 = 6 + -6

Combine like terms: -4 + -6 = -10
-10 + 13x + -3x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-10 + 13x + -3x2 = 0

Factor a trinomial.
(-10 + 3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-10 + 3x)' equal to zero and attempt to solve:

Simplifying
-10 + 3x = 0

Solving
-10 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + 3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3x = 0 + 10
3x = 0 + 10

Combine like terms: 0 + 10 = 10
3x = 10

Divide each side by '3'.
x = 3.333333333

Simplifying
x = 3.333333333

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 = {3.333333333, 1}

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