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

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


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

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

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

Multiply (2 + x) * (4 + 3x)
(2(4 + 3x) + x(4 + 3x)) = 0
((4 * 2 + 3x * 2) + x(4 + 3x)) = 0
((8 + 6x) + x(4 + 3x)) = 0
(8 + 6x + (4 * x + 3x * x)) = 0
(8 + 6x + (4x + 3x2)) = 0

Combine like terms: 6x + 4x = 10x
(8 + 10x + 3x2) = 0

Solving
8 + 10x + 3x2 = 0

Solving for variable 'x'.

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


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 '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 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 + 3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 0 + -4
3x = 0 + -4

Combine like terms: 0 + -4 = -4
3x = -4

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-2, -1.333333333}

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