(3x+1)(2x+7)=0

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Solution for (3x+1)(2x+7)=0 equation: 


Simplifying
(3x + 1)(2x + 7) = 0

Reorder the terms:
(1 + 3x)(2x + 7) = 0

Reorder the terms:
(1 + 3x)(7 + 2x) = 0

Multiply (1 + 3x) * (7 + 2x)
(1(7 + 2x) + 3x * (7 + 2x)) = 0
((7 * 1 + 2x * 1) + 3x * (7 + 2x)) = 0
((7 + 2x) + 3x * (7 + 2x)) = 0
(7 + 2x + (7 * 3x + 2x * 3x)) = 0
(7 + 2x + (21x + 6x2)) = 0

Combine like terms: 2x + 21x = 23x
(7 + 23x + 6x2) = 0

Solving
7 + 23x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + 2x)(1 + 3x) = 0


Subproblem 1
Set the factor '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, -0.3333333333}

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