6+y^2=24+3y

Solution for 6+y^2=24+3y equation:

Simplifying
6 + y2 = 24 + 3y

Solving
6 + y2 = 24 + 3y

Solving for variable 'y'.

Reorder the terms:
6 + -24 + -3y + y2 = 24 + 3y + -24 + -3y

Combine like terms: 6 + -24 = -18
-18 + -3y + y2 = 24 + 3y + -24 + -3y

Reorder the terms:
-18 + -3y + y2 = 24 + -24 + 3y + -3y

Combine like terms: 24 + -24 = 0
-18 + -3y + y2 = 0 + 3y + -3y
-18 + -3y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-18 + -3y + y2 = 0

Factor a trinomial.
(-3 + -1y)(6 + -1y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 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 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-3, 6}