x(x+2)=119+7(x+x+2)

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Solution for x(x+2)=119+7(x+x+2) equation: 


Simplifying
x(x + 2) = 119 + 7(x + x + 2)

Reorder the terms:
x(2 + x) = 119 + 7(x + x + 2)
(2 * x + x * x) = 119 + 7(x + x + 2)
(2x + x2) = 119 + 7(x + x + 2)

Reorder the terms:
2x + x2 = 119 + 7(2 + x + x)

Combine like terms: x + x = 2x
2x + x2 = 119 + 7(2 + 2x)
2x + x2 = 119 + (2 * 7 + 2x * 7)
2x + x2 = 119 + (14 + 14x)

Combine like terms: 119 + 14 = 133
2x + x2 = 133 + 14x

Solving
2x + x2 = 133 + 14x

Solving for variable 'x'.

Reorder the terms:
-133 + 2x + -14x + x2 = 133 + 14x + -133 + -14x

Combine like terms: 2x + -14x = -12x
-133 + -12x + x2 = 133 + 14x + -133 + -14x

Reorder the terms:
-133 + -12x + x2 = 133 + -133 + 14x + -14x

Combine like terms: 133 + -133 = 0
-133 + -12x + x2 = 0 + 14x + -14x
-133 + -12x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-133 + -12x + x2 = 0

Factor a trinomial.
(-7 + -1x)(19 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-7, 19}

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