(x+4)(3x+9)=0

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Solution for (x+4)(3x+9)=0 equation: 


Simplifying
(x + 4)(3x + 9) = 0

Reorder the terms:
(4 + x)(3x + 9) = 0

Reorder the terms:
(4 + x)(9 + 3x) = 0

Multiply (4 + x) * (9 + 3x)
(4(9 + 3x) + x(9 + 3x)) = 0
((9 * 4 + 3x * 4) + x(9 + 3x)) = 0
((36 + 12x) + x(9 + 3x)) = 0
(36 + 12x + (9 * x + 3x * x)) = 0
(36 + 12x + (9x + 3x2)) = 0

Combine like terms: 12x + 9x = 21x
(36 + 21x + 3x2) = 0

Solving
36 + 21x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 7x + x2) = 0

Factor a trinomial.
3((4 + x)(3 + 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 '(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 = {-4, -3}

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