(3x+8)(2x+1)=0

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Solution for (3x+8)(2x+1)=0 equation: 


Simplifying
(3x + 8)(2x + 1) = 0

Reorder the terms:
(8 + 3x)(2x + 1) = 0

Reorder the terms:
(8 + 3x)(1 + 2x) = 0

Multiply (8 + 3x) * (1 + 2x)
(8(1 + 2x) + 3x * (1 + 2x)) = 0
((1 * 8 + 2x * 8) + 3x * (1 + 2x)) = 0
((8 + 16x) + 3x * (1 + 2x)) = 0
(8 + 16x + (1 * 3x + 2x * 3x)) = 0
(8 + 16x + (3x + 6x2)) = 0

Combine like terms: 16x + 3x = 19x
(8 + 19x + 6x2) = 0

Solving
8 + 19x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + 3x)(1 + 2x) = 0


Subproblem 1
Set the factor '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-2.666666667, -0.5}

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