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

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


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

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

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

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

Combine like terms: 7x + 3x = 10x
(7 + 10x + 3x2) = 0

Solving
7 + 10x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + 3x)(1 + 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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-2.333333333, -1}

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