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

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


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

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

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

Remove parenthesis around (2 + x)
6x + 3x2 = 2 + x

Solving
6x + 3x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
-2 + 6x + -1x + 3x2 = 2 + x + -2 + -1x

Combine like terms: 6x + -1x = 5x
-2 + 5x + 3x2 = 2 + x + -2 + -1x

Reorder the terms:
-2 + 5x + 3x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
-2 + 5x + 3x2 = 0 + x + -1x
-2 + 5x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + 5x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(1 + -3x) = 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 '(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 = {-2, 0.3333333333}

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