x^2+4x+6=2x+6

Solution for x^2+4x+6=2x+6 equation:

Simplifying
x2 + 4x + 6 = 2x + 6

Reorder the terms:
6 + 4x + x2 = 2x + 6

Reorder the terms:
6 + 4x + x2 = 6 + 2x

Add '-6' to each side of the equation.
6 + 4x + -6 + x2 = 6 + -6 + 2x

Reorder the terms:
6 + -6 + 4x + x2 = 6 + -6 + 2x

Combine like terms: 6 + -6 = 0
0 + 4x + x2 = 6 + -6 + 2x
4x + x2 = 6 + -6 + 2x

Combine like terms: 6 + -6 = 0
4x + x2 = 0 + 2x
4x + x2 = 2x

Solving
4x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
4x + -2x + x2 = 2x + -2x

Combine like terms: 4x + -2x = 2x
2x + x2 = 2x + -2x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {0, -2}