(3x-6)(2x-10)=0

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Solution for (3x-6)(2x-10)=0 equation: 


Simplifying
(3x + -6)(2x + -10) = 0

Reorder the terms:
(-6 + 3x)(2x + -10) = 0

Reorder the terms:
(-6 + 3x)(-10 + 2x) = 0

Multiply (-6 + 3x) * (-10 + 2x)
(-6(-10 + 2x) + 3x * (-10 + 2x)) = 0
((-10 * -6 + 2x * -6) + 3x * (-10 + 2x)) = 0
((60 + -12x) + 3x * (-10 + 2x)) = 0
(60 + -12x + (-10 * 3x + 2x * 3x)) = 0
(60 + -12x + (-30x + 6x2)) = 0

Combine like terms: -12x + -30x = -42x
(60 + -42x + 6x2) = 0

Solving
60 + -42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + -7x + x2) = 0

Factor a trinomial.
6((2 + -1x)(5 + -1x)) = 0

Ignore the factor 6.

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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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