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

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


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

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

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

Multiply (1 + 2x) * (7 + 3x)
(1(7 + 3x) + 2x * (7 + 3x)) = 0
((7 * 1 + 3x * 1) + 2x * (7 + 3x)) = 0
((7 + 3x) + 2x * (7 + 3x)) = 0
(7 + 3x + (7 * 2x + 3x * 2x)) = 0
(7 + 3x + (14x + 6x2)) = 0

Combine like terms: 3x + 14x = 17x
(7 + 17x + 6x2) = 0

Solving
7 + 17x + 6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333

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 = {-2.333333333, -0.5}

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