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

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


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

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

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

Multiply (4 + 2X) * (1 + 3X)
(4(1 + 3X) + 2X * (1 + 3X)) = 0
((1 * 4 + 3X * 4) + 2X * (1 + 3X)) = 0
((4 + 12X) + 2X * (1 + 3X)) = 0
(4 + 12X + (1 * 2X + 3X * 2X)) = 0
(4 + 12X + (2X + 6X2)) = 0

Combine like terms: 12X + 2X = 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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