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

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


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

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

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

Multiply (-5 + 3x) * (-1 + 2x)
(-5(-1 + 2x) + 3x * (-1 + 2x)) = 5
((-1 * -5 + 2x * -5) + 3x * (-1 + 2x)) = 5
((5 + -10x) + 3x * (-1 + 2x)) = 5
(5 + -10x + (-1 * 3x + 2x * 3x)) = 5
(5 + -10x + (-3x + 6x2)) = 5

Combine like terms: -10x + -3x = -13x
(5 + -13x + 6x2) = 5

Add '-5' to each side of the equation.
5 + -13x + -5 + 6x2 = 5 + -5

Reorder the terms:
5 + -5 + -13x + 6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
0 + -13x + 6x2 = 5 + -5
-13x + 6x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-13x + 6x2 = 0

Solving
-13x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13 + 6x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-13 + 6x)' equal to zero and attempt to solve:

Simplifying
-13 + 6x = 0

Solving
-13 + 6x = 0

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

Add '13' to each side of the equation.
-13 + 13 + 6x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 6x = 0 + 13
6x = 0 + 13

Combine like terms: 0 + 13 = 13
6x = 13

Divide each side by '6'.
x = 2.166666667

Simplifying
x = 2.166666667
Solution
x = {0, 2.166666667}

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