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

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


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

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

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

Combine like terms: x + x = 2x
2x + x2 = 6 + 3(2 + 2x)
2x + x2 = 6 + (2 * 3 + 2x * 3)
2x + x2 = 6 + (6 + 6x)

Combine like terms: 6 + 6 = 12
2x + x2 = 12 + 6x

Solving
2x + x2 = 12 + 6x

Solving for variable 'x'.

Reorder the terms:
-12 + 2x + -6x + x2 = 12 + 6x + -12 + -6x

Combine like terms: 2x + -6x = -4x
-12 + -4x + x2 = 12 + 6x + -12 + -6x

Reorder the terms:
-12 + -4x + x2 = 12 + -12 + 6x + -6x

Combine like terms: 12 + -12 = 0
-12 + -4x + x2 = 0 + 6x + -6x
-12 + -4x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-12 + -4x + x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}

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