2(x-6)(20-3x)=0

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Solution for 2(x-6)(20-3x)=0 equation: 


Simplifying
2(x + -6)(20 + -3x) = 0

Reorder the terms:
2(-6 + x)(20 + -3x) = 0

Multiply (-6 + x) * (20 + -3x)
2(-6(20 + -3x) + x(20 + -3x)) = 0
2((20 * -6 + -3x * -6) + x(20 + -3x)) = 0
2((-120 + 18x) + x(20 + -3x)) = 0
2(-120 + 18x + (20 * x + -3x * x)) = 0
2(-120 + 18x + (20x + -3x2)) = 0

Combine like terms: 18x + 20x = 38x
2(-120 + 38x + -3x2) = 0
(-120 * 2 + 38x * 2 + -3x2 * 2) = 0
(-240 + 76x + -6x2) = 0

Solving
-240 + 76x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-120 + 38x + -3x2) = 0

Factor a trinomial.
2((-20 + 3x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6.666666667, 6}

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