x^2+8x+30=3x+24

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Solution for x^2+8x+30=3x+24 equation: 


Simplifying
x2 + 8x + 30 = 3x + 24

Reorder the terms:
30 + 8x + x2 = 3x + 24

Reorder the terms:
30 + 8x + x2 = 24 + 3x

Solving
30 + 8x + x2 = 24 + 3x

Solving for variable 'x'.

Reorder the terms:
30 + -24 + 8x + -3x + x2 = 24 + 3x + -24 + -3x

Combine like terms: 30 + -24 = 6
6 + 8x + -3x + x2 = 24 + 3x + -24 + -3x

Combine like terms: 8x + -3x = 5x
6 + 5x + x2 = 24 + 3x + -24 + -3x

Reorder the terms:
6 + 5x + x2 = 24 + -24 + 3x + -3x

Combine like terms: 24 + -24 = 0
6 + 5x + x2 = 0 + 3x + -3x
6 + 5x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
6 + 5x + x2 = 0

Factor a trinomial.
(3 + x)(2 + x) = 0


Subproblem 1
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

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-3, -2}

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