0=6x(1-x)

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Solution for 0=6x(1-x) equation: 


Simplifying
0 = 6x(1 + -1x)
0 = (1 * 6x + -1x * 6x)
0 = (6x + -6x2)

Solving
0 = 6x + -6x2

Solving for variable 'x'.
Remove the zero:
-6x + 6x2 = 6x + -6x2 + -6x + 6x2

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

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

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

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-1 + x) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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