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

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


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

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

Multiply (1 + 3y) * (7 + y)
(1(7 + y) + 3y * (7 + y)) = 0
((7 * 1 + y * 1) + 3y * (7 + y)) = 0
((7 + 1y) + 3y * (7 + y)) = 0
(7 + 1y + (7 * 3y + y * 3y)) = 0
(7 + 1y + (21y + 3y2)) = 0

Combine like terms: 1y + 21y = 22y
(7 + 22y + 3y2) = 0

Solving
7 + 22y + 3y2 = 0

Solving for variable 'y'.

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


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

Simplifying
7 + y = 0

Solving
7 + y = 0

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

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

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

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

Simplifying
y = -7

Subproblem 2
Set the factor '(1 + 3y)' equal to zero and attempt to solve:

Simplifying
1 + 3y = 0

Solving
1 + 3y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3y = 0 + -1
3y = 0 + -1

Combine like terms: 0 + -1 = -1
3y = -1

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {-7, -0.3333333333}

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