(2x-6)(3x-5)=0

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Solution for (2x-6)(3x-5)=0 equation: 


Simplifying
(2x + -6)(3x + -5) = 0

Reorder the terms:
(-6 + 2x)(3x + -5) = 0

Reorder the terms:
(-6 + 2x)(-5 + 3x) = 0

Multiply (-6 + 2x) * (-5 + 3x)
(-6(-5 + 3x) + 2x * (-5 + 3x)) = 0
((-5 * -6 + 3x * -6) + 2x * (-5 + 3x)) = 0
((30 + -18x) + 2x * (-5 + 3x)) = 0
(30 + -18x + (-5 * 2x + 3x * 2x)) = 0
(30 + -18x + (-10x + 6x2)) = 0

Combine like terms: -18x + -10x = -28x
(30 + -28x + 6x2) = 0

Solving
30 + -28x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -14x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.666666667, 3}

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