(25r^2+10r+1)=0

Solution for (25r^2+10r+1)=0 equation:

Simplifying
(25r2 + 10r + 1) = 0

Reorder the terms:
(1 + 10r + 25r2) = 0

Remove parenthesis around (1 + 10r + 25r2)
1 + 10r + 25r2 = 0

Solving
1 + 10r + 25r2 = 0

Solving for variable 'r'.

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

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

Simplifying
1 + 5r = 0

Solving
1 + 5r = 0

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

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

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

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

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

Simplifying
r = -0.2
Subproblem 2
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 0

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

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

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

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

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

Simplifying
r = -0.2
Solution
r = {-0.2, -0.2}