(3x-1)(5-2x)=6

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Solution for (3x-1)(5-2x)=6 equation: 


Simplifying
(3x + -1)(5 + -2x) = 6

Reorder the terms:
(-1 + 3x)(5 + -2x) = 6

Multiply (-1 + 3x) * (5 + -2x)
(-1(5 + -2x) + 3x * (5 + -2x)) = 6
((5 * -1 + -2x * -1) + 3x * (5 + -2x)) = 6
((-5 + 2x) + 3x * (5 + -2x)) = 6
(-5 + 2x + (5 * 3x + -2x * 3x)) = 6
(-5 + 2x + (15x + -6x2)) = 6

Combine like terms: 2x + 15x = 17x
(-5 + 17x + -6x2) = 6

Solving
-5 + 17x + -6x2 = 6

Solving for variable 'x'.

Reorder the terms:
-5 + -6 + 17x + -6x2 = 6 + -6

Combine like terms: -5 + -6 = -11
-11 + 17x + -6x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-11 + 17x + -6x2 = 0

Factor a trinomial.
(-11 + 6x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-11 + 6x)' equal to zero and attempt to solve:

Simplifying
-11 + 6x = 0

Solving
-11 + 6x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 6x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 6x = 0 + 11
6x = 0 + 11

Combine like terms: 0 + 11 = 11
6x = 11

Divide each side by '6'.
x = 1.833333333

Simplifying
x = 1.833333333

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 = {1.833333333, 1}

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