y(3y+7)=-4

Solution for y(3y+7)=-4 equation:

Simplifying
y(3y + 7) = -4

Reorder the terms:
y(7 + 3y) = -4
(7 * y + 3y * y) = -4
(7y + 3y2) = -4

Solving
7y + 3y2 = -4

Solving for variable 'y'.

Reorder the terms:
4 + 7y + 3y2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 7y + 3y2 = 0

Factor a trinomial.
(4 + 3y)(1 + y) = 0

Subproblem 1
Set the factor '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {-1.333333333, -1}