2x+6=2x^2+6

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

Simplifying
2x + 6 = 2x2 + 6

Reorder the terms:
6 + 2x = 2x2 + 6

Reorder the terms:
6 + 2x = 6 + 2x2

Add '-6' to each side of the equation.
6 + -6 + 2x = 6 + -6 + 2x2

Combine like terms: 6 + -6 = 0
0 + 2x = 6 + -6 + 2x2
2x = 6 + -6 + 2x2

Combine like terms: 6 + -6 = 0
2x = 0 + 2x2
2x = 2x2

Solving
2x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -1x) = 0

Ignore the factor 2.
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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 1

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