10y^2+9y+2=0

Solution for 10y^2+9y+2=0 equation:

Simplifying
10y2 + 9y + 2 = 0

Reorder the terms:
2 + 9y + 10y2 = 0

Solving
2 + 9y + 10y2 = 0

Solving for variable 'y'.

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

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

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
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 = {-0.5, -0.4}