(3x-5)(4x-2)=0

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Solution for (3x-5)(4x-2)=0 equation: 


Simplifying
(3x + -5)(4x + -2) = 0

Reorder the terms:
(-5 + 3x)(4x + -2) = 0

Reorder the terms:
(-5 + 3x)(-2 + 4x) = 0

Multiply (-5 + 3x) * (-2 + 4x)
(-5(-2 + 4x) + 3x * (-2 + 4x)) = 0
((-2 * -5 + 4x * -5) + 3x * (-2 + 4x)) = 0
((10 + -20x) + 3x * (-2 + 4x)) = 0
(10 + -20x + (-2 * 3x + 4x * 3x)) = 0
(10 + -20x + (-6x + 12x2)) = 0

Combine like terms: -20x + -6x = -26x
(10 + -26x + 12x2) = 0

Solving
10 + -26x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -13x + 6x2) = 0

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

Ignore the factor 2.

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 '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0.5, 1.666666667}

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