(x+2+2)(3x+1+2)=0

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Solution for (x+2+2)(3x+1+2)=0 equation: 


Simplifying
(x + 2 + 2)(3x + 1 + 2) = 0

Reorder the terms:
(2 + 2 + x)(3x + 1 + 2) = 0

Combine like terms: 2 + 2 = 4
(4 + x)(3x + 1 + 2) = 0

Reorder the terms:
(4 + x)(1 + 2 + 3x) = 0

Combine like terms: 1 + 2 = 3
(4 + x)(3 + 3x) = 0

Multiply (4 + x) * (3 + 3x)
(4(3 + 3x) + x(3 + 3x)) = 0
((3 * 4 + 3x * 4) + x(3 + 3x)) = 0
((12 + 12x) + x(3 + 3x)) = 0
(12 + 12x + (3 * x + 3x * x)) = 0
(12 + 12x + (3x + 3x2)) = 0

Combine like terms: 12x + 3x = 15x
(12 + 15x + 3x2) = 0

Solving
12 + 15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 5x + x2) = 0

Factor a trinomial.
3((4 + x)(1 + x)) = 0

Ignore the factor 3.

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-4, -1}

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