x(x+1)=2x+6

Solution for x(x+1)=2x+6 equation:

Simplifying
x(x + 1) = 2x + 6

Reorder the terms:
x(1 + x) = 2x + 6
(1 * x + x * x) = 2x + 6
(1x + x2) = 2x + 6

Reorder the terms:
1x + x2 = 6 + 2x

Solving
1x + x2 = 6 + 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 1x + -2x + x2 = 6 + 2x + -6 + -2x

Combine like terms: 1x + -2x = -1x
-6 + -1x + x2 = 6 + 2x + -6 + -2x

Reorder the terms:
-6 + -1x + x2 = 6 + -6 + 2x + -2x

Combine like terms: 6 + -6 = 0
-6 + -1x + x2 = 0 + 2x + -2x
-6 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + -1x + x2 = 0

Factor a trinomial.
(-2 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}