8=(x+3)+x^2+3x

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Solution for 8=(x+3)+x^2+3x equation: 


Simplifying
8 = (x + 3) + x2 + 3x

Reorder the terms:
8 = (3 + x) + x2 + 3x

Remove parenthesis around (3 + x)
8 = 3 + x + x2 + 3x

Reorder the terms:
8 = 3 + x + 3x + x2

Combine like terms: x + 3x = 4x
8 = 3 + 4x + x2

Solving
8 = 3 + 4x + x2

Solving for variable 'x'.

Combine like terms: 8 + -3 = 5
5 + -4x + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2

Reorder the terms:
5 + -4x + -1x2 = 3 + -3 + 4x + -4x + x2 + -1x2

Combine like terms: 3 + -3 = 0
5 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
5 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
5 + -4x + -1x2 = 0 + x2 + -1x2
5 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + -4x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(5 + 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {1, -5}

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