x(x+2)=111+3(x+x+2)

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Solution for x(x+2)=111+3(x+x+2) equation: 


Simplifying
x(x + 2) = 111 + 3(x + x + 2)

Reorder the terms:
x(2 + x) = 111 + 3(x + x + 2)
(2 * x + x * x) = 111 + 3(x + x + 2)
(2x + x2) = 111 + 3(x + x + 2)

Reorder the terms:
2x + x2 = 111 + 3(2 + x + x)

Combine like terms: x + x = 2x
2x + x2 = 111 + 3(2 + 2x)
2x + x2 = 111 + (2 * 3 + 2x * 3)
2x + x2 = 111 + (6 + 6x)

Combine like terms: 111 + 6 = 117
2x + x2 = 117 + 6x

Solving
2x + x2 = 117 + 6x

Solving for variable 'x'.

Reorder the terms:
-117 + 2x + -6x + x2 = 117 + 6x + -117 + -6x

Combine like terms: 2x + -6x = -4x
-117 + -4x + x2 = 117 + 6x + -117 + -6x

Reorder the terms:
-117 + -4x + x2 = 117 + -117 + 6x + -6x

Combine like terms: 117 + -117 = 0
-117 + -4x + x2 = 0 + 6x + -6x
-117 + -4x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-117 + -4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(13 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-9, 13}

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