(2x-10)(3x-20)=0

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Solution for (2x-10)(3x-20)=0 equation: 


Simplifying
(2x + -10)(3x + -20) = 0

Reorder the terms:
(-10 + 2x)(3x + -20) = 0

Reorder the terms:
(-10 + 2x)(-20 + 3x) = 0

Multiply (-10 + 2x) * (-20 + 3x)
(-10(-20 + 3x) + 2x * (-20 + 3x)) = 0
((-20 * -10 + 3x * -10) + 2x * (-20 + 3x)) = 0
((200 + -30x) + 2x * (-20 + 3x)) = 0
(200 + -30x + (-20 * 2x + 3x * 2x)) = 0
(200 + -30x + (-40x + 6x2)) = 0

Combine like terms: -30x + -40x = -70x
(200 + -70x + 6x2) = 0

Solving
200 + -70x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(100 + -35x + 3x2) = 0

Factor a trinomial.
2((5 + -1x)(20 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(20 + -3x)' equal to zero and attempt to solve:

Simplifying
20 + -3x = 0

Solving
20 + -3x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3x = 0 + -20
-3x = 0 + -20

Combine like terms: 0 + -20 = -20
-3x = -20

Divide each side by '-3'.
x = 6.666666667

Simplifying
x = 6.666666667
Solution
x = {5, 6.666666667}

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