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

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


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

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

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

Combine like terms: 4x + 6x = 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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