3(3x+2)(x+4)=0

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Solution for 3(3x+2)(x+4)=0 equation:


Simplifying
3(3x + 2)(x + 4) = 0

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

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

Multiply (2 + 3x) * (4 + x)
3(2(4 + x) + 3x * (4 + x)) = 0
3((4 * 2 + x * 2) + 3x * (4 + x)) = 0
3((8 + 2x) + 3x * (4 + x)) = 0
3(8 + 2x + (4 * 3x + x * 3x)) = 0
3(8 + 2x + (12x + 3x2)) = 0

Combine like terms: 2x + 12x = 14x
3(8 + 14x + 3x2) = 0
(8 * 3 + 14x * 3 + 3x2 * 3) = 0
(24 + 42x + 9x2) = 0

Solving
24 + 42x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 14x + 3x2) = 0

Factor a trinomial.
3((4 + x)(2 + 3x)) = 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {-4, -0.6666666667}

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