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

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


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

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

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

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

Combine like terms: 6x + 7x = 13x
(14 + 13x + 3x2) = 0

Solving
14 + 13x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + 3x)(2 + x) = 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 '(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
Solution
x = {-2.333333333, -2}

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