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

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


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

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

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

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

Combine like terms: 3x + 4x = 7x
(2 + 7x + 6x2) = 0

Solving
2 + 7x + 6x2 = 0

Solving for variable 'x'.

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


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

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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 = {-0.6666666667, -0.5}

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