12x-3x^2-6x(x+1)=

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Solution for 12x-3x^2-6x(x+1)= equation: 


Simplifying
12x + -3x2 + -6x(x + 1) = 0

Reorder the terms:
12x + -3x2 + -6x(1 + x) = 0
12x + -3x2 + (1 * -6x + x * -6x) = 0
12x + -3x2 + (-6x + -6x2) = 0

Reorder the terms:
12x + -6x + -3x2 + -6x2 = 0

Combine like terms: 12x + -6x = 6x
6x + -3x2 + -6x2 = 0

Combine like terms: -3x2 + -6x2 = -9x2
6x + -9x2 = 0

Solving
6x + -9x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, 0.6666666667}

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