7y+7y(y+3)=-21

Solution for 7y+7y(y+3)=-21 equation:

Simplifying
7y + 7y(y + 3) = -21

Reorder the terms:
7y + 7y(3 + y) = -21
7y + (3 * 7y + y * 7y) = -21
7y + (21y + 7y2) = -21

Combine like terms: 7y + 21y = 28y
28y + 7y2 = -21

Solving
28y + 7y2 = -21

Solving for variable 'y'.

Reorder the terms:
21 + 28y + 7y2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + 28y + 7y2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(3 + 4y + y2) = 0

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

Ignore the factor 7.
Subproblem 1
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

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

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

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

Simplifying
y = -3
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 = {-3, -1}