0=3y^2+24y+45

Solution for 0=3y^2+24y+45 equation:

Simplifying
0 = 3y2 + 24y + 45

Reorder the terms:
0 = 45 + 24y + 3y2

Solving
0 = 45 + 24y + 3y2

Solving for variable 'y'.

Combine like terms: 0 + -45 = -45
-45 + -24y + -3y2 = 45 + 24y + 3y2 + -45 + -24y + -3y2

Reorder the terms:
-45 + -24y + -3y2 = 45 + -45 + 24y + -24y + 3y2 + -3y2

Combine like terms: 45 + -45 = 0
-45 + -24y + -3y2 = 0 + 24y + -24y + 3y2 + -3y2
-45 + -24y + -3y2 = 24y + -24y + 3y2 + -3y2

Combine like terms: 24y + -24y = 0
-45 + -24y + -3y2 = 0 + 3y2 + -3y2
-45 + -24y + -3y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-45 + -24y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(15 + 8y + y2) = 0

Factor a trinomial.
-3((5 + y)(3 + y)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Subproblem 2
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
Solution
y = {-5, -3}