4r^2+25r+25=0

Solution for 4r^2+25r+25=0 equation:

Simplifying
4r2 + 25r + 25 = 0

Reorder the terms:
25 + 25r + 4r2 = 0

Solving
25 + 25r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + r)(5 + 4r) = 0

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

Simplifying
5 + r = 0

Solving
5 + r = 0

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

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

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

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

Simplifying
r = -5
Subproblem 2
Set the factor '(5 + 4r)' equal to zero and attempt to solve:

Simplifying
5 + 4r = 0

Solving
5 + 4r = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4r = 0 + -5
4r = 0 + -5

Combine like terms: 0 + -5 = -5
4r = -5

Divide each side by '4'.
r = -1.25

Simplifying
r = -1.25
Solution
r = {-5, -1.25}