y(y+4)=21

Solution for y(y+4)=21 equation:

Simplifying
y(y + 4) = 21

Reorder the terms:
y(4 + y) = 21
(4 * y + y * y) = 21
(4y + y2) = 21

Solving
4y + y2 = 21

Solving for variable 'y'.

Reorder the terms:
-21 + 4y + y2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 4y + y2 = 0

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

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

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 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 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-7, 3}