5y^2+15y+4=2y+10

Solution for 5y^2+15y+4=2y+10 equation:

Simplifying
5y2 + 15y + 4 = 2y + 10

Reorder the terms:
4 + 15y + 5y2 = 2y + 10

Reorder the terms:
4 + 15y + 5y2 = 10 + 2y

Solving
4 + 15y + 5y2 = 10 + 2y

Solving for variable 'y'.

Reorder the terms:
4 + -10 + 15y + -2y + 5y2 = 10 + 2y + -10 + -2y

Combine like terms: 4 + -10 = -6
-6 + 15y + -2y + 5y2 = 10 + 2y + -10 + -2y

Combine like terms: 15y + -2y = 13y
-6 + 13y + 5y2 = 10 + 2y + -10 + -2y

Reorder the terms:
-6 + 13y + 5y2 = 10 + -10 + 2y + -2y

Combine like terms: 10 + -10 = 0
-6 + 13y + 5y2 = 0 + 2y + -2y
-6 + 13y + 5y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-6 + 13y + 5y2 = 0

Factor a trinomial.
(-3 + -1y)(2 + -5y) = 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 '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

Solving
2 + -5y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {-3, 0.4}