5y^2+46y+105=0

Solution for 5y^2+46y+105=0 equation:

Simplifying
5y2 + 46y + 105 = 0

Reorder the terms:
105 + 46y + 5y2 = 0

Solving
105 + 46y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + y)(21 + 5y) = 0

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 '(21 + 5y)' equal to zero and attempt to solve:

Simplifying
21 + 5y = 0

Solving
21 + 5y = 0

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

Add '-21' to each side of the equation.
21 + -21 + 5y = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 5y = 0 + -21
5y = 0 + -21

Combine like terms: 0 + -21 = -21
5y = -21

Divide each side by '5'.
y = -4.2

Simplifying
y = -4.2
Solution
y = {-5, -4.2}