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

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


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

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

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

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

Combine like terms: 1x + 21x = 22x
(7 + 22x + 3x2) = 0

Solving
7 + 22x + 3x2 = 0

Solving for variable 'x'.

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


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

Simplifying
7 + x = 0

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

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

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

Simplifying
x = -7

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 = {-7, -0.3333333333}

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