10y^2+27y+5=0

Solution for 10y^2+27y+5=0 equation:

Simplifying
10y2 + 27y + 5 = 0

Reorder the terms:
5 + 27y + 10y2 = 0

Solving
5 + 27y + 10y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + 2y)(1 + 5y) = 0

Subproblem 1
Set the factor '(5 + 2y)' equal to zero and attempt to solve:

Simplifying
5 + 2y = 0

Solving
5 + 2y = 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 + 2y = 0 + -5

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

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

Divide each side by '2'.
y = -2.5

Simplifying
y = -2.5
Subproblem 2
Set the factor '(1 + 5y)' equal to zero and attempt to solve:

Simplifying
1 + 5y = 0

Solving
1 + 5y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y = 0 + -1
5y = 0 + -1

Combine like terms: 0 + -1 = -1
5y = -1

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Solution
y = {-2.5, -0.2}