(2x-1)(3x-7)=2

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Solution for (2x-1)(3x-7)=2 equation: 


Simplifying
(2x + -1)(3x + -7) = 2

Reorder the terms:
(-1 + 2x)(3x + -7) = 2

Reorder the terms:
(-1 + 2x)(-7 + 3x) = 2

Multiply (-1 + 2x) * (-7 + 3x)
(-1(-7 + 3x) + 2x * (-7 + 3x)) = 2
((-7 * -1 + 3x * -1) + 2x * (-7 + 3x)) = 2
((7 + -3x) + 2x * (-7 + 3x)) = 2
(7 + -3x + (-7 * 2x + 3x * 2x)) = 2
(7 + -3x + (-14x + 6x2)) = 2

Combine like terms: -3x + -14x = -17x
(7 + -17x + 6x2) = 2

Solving
7 + -17x + 6x2 = 2

Solving for variable 'x'.

Reorder the terms:
7 + -2 + -17x + 6x2 = 2 + -2

Combine like terms: 7 + -2 = 5
5 + -17x + 6x2 = 2 + -2

Combine like terms: 2 + -2 = 0
5 + -17x + 6x2 = 0

Factor a trinomial.
(1 + -3x)(5 + -2x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.3333333333, 2.5}

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