(3x-7)(2x-4)=0

Solution for (3x-7)(2x-4)=0 equation:

Simplifying
(3x + -7)(2x + -4) = 0

Reorder the terms:
(-7 + 3x)(2x + -4) = 0

Reorder the terms:
(-7 + 3x)(-4 + 2x) = 0

Multiply (-7 + 3x) * (-4 + 2x)
(-7(-4 + 2x) + 3x * (-4 + 2x)) = 0
((-4 * -7 + 2x * -7) + 3x * (-4 + 2x)) = 0
((28 + -14x) + 3x * (-4 + 2x)) = 0
(28 + -14x + (-4 * 3x + 2x * 3x)) = 0
(28 + -14x + (-12x + 6x2)) = 0

Combine like terms: -14x + -12x = -26x
(28 + -26x + 6x2) = 0

Solving
28 + -26x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -13x + 3x2) = 0

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, 2.333333333}