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

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


Simplifying
3(x2 + -2x) + 3(3x2 + 2) = 3x2 + 6

Reorder the terms:
3(-2x + x2) + 3(3x2 + 2) = 3x2 + 6
(-2x * 3 + x2 * 3) + 3(3x2 + 2) = 3x2 + 6
(-6x + 3x2) + 3(3x2 + 2) = 3x2 + 6

Reorder the terms:
-6x + 3x2 + 3(2 + 3x2) = 3x2 + 6
-6x + 3x2 + (2 * 3 + 3x2 * 3) = 3x2 + 6
-6x + 3x2 + (6 + 9x2) = 3x2 + 6

Reorder the terms:
6 + -6x + 3x2 + 9x2 = 3x2 + 6

Combine like terms: 3x2 + 9x2 = 12x2
6 + -6x + 12x2 = 3x2 + 6

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

Add '-6' to each side of the equation.
6 + -6x + -6 + 12x2 = 6 + -6 + 3x2

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

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

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

Solving
-6x + 12x2 = 3x2

Solving for variable 'x'.

Combine like terms: 12x2 + -3x2 = 9x2
-6x + 9x2 = 3x2 + -3x2

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

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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