(3x+1)(2x+4)=0

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Solution for (3x+1)(2x+4)=0 equation: 


Simplifying
(3x + 1)(2x + 4) = 0

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

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

Multiply (1 + 3x) * (4 + 2x)
(1(4 + 2x) + 3x * (4 + 2x)) = 0
((4 * 1 + 2x * 1) + 3x * (4 + 2x)) = 0
((4 + 2x) + 3x * (4 + 2x)) = 0
(4 + 2x + (4 * 3x + 2x * 3x)) = 0
(4 + 2x + (12x + 6x2)) = 0

Combine like terms: 2x + 12x = 14x
(4 + 14x + 6x2) = 0

Solving
4 + 14x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 7x + 3x2) = 0

Factor a trinomial.
2((2 + x)(1 + 3x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-2, -0.3333333333}

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