x+6=6+3x^2

Solution for x+6=6+3x^2 equation:

Simplifying
x + 6 = 6 + 3x2

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

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

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

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

Solving
x = 3x2

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -3x) = 0

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, 0.3333333333}