(x^2+8)+(3x+6)=24

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Solution for (x^2+8)+(3x+6)=24 equation: 


Simplifying
(x2 + 8) + (3x + 6) = 24

Reorder the terms:
(8 + x2) + (3x + 6) = 24

Remove parenthesis around (8 + x2)
8 + x2 + (3x + 6) = 24

Reorder the terms:
8 + x2 + (6 + 3x) = 24

Remove parenthesis around (6 + 3x)
8 + x2 + 6 + 3x = 24

Reorder the terms:
8 + 6 + 3x + x2 = 24

Combine like terms: 8 + 6 = 14
14 + 3x + x2 = 24

Solving
14 + 3x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
14 + -24 + 3x + x2 = 24 + -24

Combine like terms: 14 + -24 = -10
-10 + 3x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-10 + 3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 0


Subproblem 1
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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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