x(x+2)=219+6(x+x+2)

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Solution for x(x+2)=219+6(x+x+2) equation: 


Simplifying
x(x + 2) = 219 + 6(x + x + 2)

Reorder the terms:
x(2 + x) = 219 + 6(x + x + 2)
(2 * x + x * x) = 219 + 6(x + x + 2)
(2x + x2) = 219 + 6(x + x + 2)

Reorder the terms:
2x + x2 = 219 + 6(2 + x + x)

Combine like terms: x + x = 2x
2x + x2 = 219 + 6(2 + 2x)
2x + x2 = 219 + (2 * 6 + 2x * 6)
2x + x2 = 219 + (12 + 12x)

Combine like terms: 219 + 12 = 231
2x + x2 = 231 + 12x

Solving
2x + x2 = 231 + 12x

Solving for variable 'x'.

Reorder the terms:
-231 + 2x + -12x + x2 = 231 + 12x + -231 + -12x

Combine like terms: 2x + -12x = -10x
-231 + -10x + x2 = 231 + 12x + -231 + -12x

Reorder the terms:
-231 + -10x + x2 = 231 + -231 + 12x + -12x

Combine like terms: 231 + -231 = 0
-231 + -10x + x2 = 0 + 12x + -12x
-231 + -10x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-231 + -10x + x2 = 0

Factor a trinomial.
(-11 + -1x)(21 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-11, 21}

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