3y-24=y(y+13)

Solution for 3y-24=y(y+13) equation:

Simplifying
3y + -24 = y(y + 13)

Reorder the terms:
-24 + 3y = y(y + 13)

Reorder the terms:
-24 + 3y = y(13 + y)
-24 + 3y = (13 * y + y * y)
-24 + 3y = (13y + y2)

Solving
-24 + 3y = 13y + y2

Solving for variable 'y'.

Combine like terms: 3y + -13y = -10y
-24 + -10y + -1y2 = 13y + y2 + -13y + -1y2

Reorder the terms:
-24 + -10y + -1y2 = 13y + -13y + y2 + -1y2

Combine like terms: 13y + -13y = 0
-24 + -10y + -1y2 = 0 + y2 + -1y2
-24 + -10y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-24 + -10y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 10y + y2) = 0

Factor a trinomial.
-1((6 + y)(4 + y)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 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 + y = 0 + -4

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

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

Simplifying
y = -4
Solution
y = {-6, -4}