(3x-7)(2x-1)=0

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Solution for (3x-7)(2x-1)=0 equation: 


Simplifying
(3x + -7)(2x + -1) = 0

Reorder the terms:
(-7 + 3x)(2x + -1) = 0

Reorder the terms:
(-7 + 3x)(-1 + 2x) = 0

Multiply (-7 + 3x) * (-1 + 2x)
(-7(-1 + 2x) + 3x * (-1 + 2x)) = 0
((-1 * -7 + 2x * -7) + 3x * (-1 + 2x)) = 0
((7 + -14x) + 3x * (-1 + 2x)) = 0
(7 + -14x + (-1 * 3x + 2x * 3x)) = 0
(7 + -14x + (-3x + 6x2)) = 0

Combine like terms: -14x + -3x = -17x
(7 + -17x + 6x2) = 0

Solving
7 + -17x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -2x)(7 + -3x) = 0


Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {0.5, 2.333333333}

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