x+(x+3)=x*(x+3)+x

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Solution for x+(x+3)=x*(x+3)+x equation: 


Simplifying
x + (x + 3) = x(x + 3) + x

Reorder the terms:
x + (3 + x) = x(x + 3) + x

Remove parenthesis around (3 + x)
x + 3 + x = x(x + 3) + x

Reorder the terms:
3 + x + x = x(x + 3) + x

Combine like terms: x + x = 2x
3 + 2x = x(x + 3) + x

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

Reorder the terms:
3 + 2x = 3x + x + x2

Combine like terms: 3x + x = 4x
3 + 2x = 4x + x2

Solving
3 + 2x = 4x + x2

Solving for variable 'x'.

Combine like terms: 2x + -4x = -2x
3 + -2x + -1x2 = 4x + x2 + -4x + -1x2

Reorder the terms:
3 + -2x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
3 + -2x + -1x2 = 0 + x2 + -1x2
3 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -2x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(3 + x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1, -3}

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