25y^2=-10y-1

Solution for 25y^2=-10y-1 equation:

Simplifying
25y2 = -10y + -1

Reorder the terms:
25y2 = -1 + -10y

Solving
25y2 = -1 + -10y

Solving for variable 'y'.

Reorder the terms:
1 + 10y + 25y2 = -1 + -10y + 1 + 10y

Reorder the terms:
1 + 10y + 25y2 = -1 + 1 + -10y + 10y

Combine like terms: -1 + 1 = 0
1 + 10y + 25y2 = 0 + -10y + 10y
1 + 10y + 25y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
1 + 10y + 25y2 = 0

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

Subproblem 1
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
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 = {-0.2, -0.2}