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

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


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

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

Multiply (-6 + x) * (20 + -3x)
0 = 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))

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

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

Solving for variable 'x'.

Combine like terms: 0 + 240 = 240
240 + -76x + 6x2 = -240 + 76x + -6x2 + 240 + -76x + 6x2

Reorder the terms:
240 + -76x + 6x2 = -240 + 240 + 76x + -76x + -6x2 + 6x2

Combine like terms: -240 + 240 = 0
240 + -76x + 6x2 = 0 + 76x + -76x + -6x2 + 6x2
240 + -76x + 6x2 = 76x + -76x + -6x2 + 6x2

Combine like terms: 76x + -76x = 0
240 + -76x + 6x2 = 0 + -6x2 + 6x2
240 + -76x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
240 + -76x + 6x2 = 0

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

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

Ignore the factor 2.

Subproblem 1
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

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 = {6, 6.666666667}

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