x(x+1)=x+(x+1)+19

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Solution for x(x+1)=x+(x+1)+19 equation: 


Simplifying
x(x + 1) = x + (x + 1) + 19

Reorder the terms:
x(1 + x) = x + (x + 1) + 19
(1 * x + x * x) = x + (x + 1) + 19
(1x + x2) = x + (x + 1) + 19

Reorder the terms:
1x + x2 = x + (1 + x) + 19

Remove parenthesis around (1 + x)
1x + x2 = x + 1 + x + 19

Reorder the terms:
1x + x2 = 1 + 19 + x + x

Combine like terms: 1 + 19 = 20
1x + x2 = 20 + x + x

Combine like terms: x + x = 2x
1x + x2 = 20 + 2x

Solving
1x + x2 = 20 + 2x

Solving for variable 'x'.

Reorder the terms:
-20 + 1x + -2x + x2 = 20 + 2x + -20 + -2x

Combine like terms: 1x + -2x = -1x
-20 + -1x + x2 = 20 + 2x + -20 + -2x

Reorder the terms:
-20 + -1x + x2 = 20 + -20 + 2x + -2x

Combine like terms: 20 + -20 = 0
-20 + -1x + x2 = 0 + 2x + -2x
-20 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-4, 5}

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