(5r+2)(r+2)=0

Solution for (5r+2)(r+2)=0 equation:

Simplifying
(5r + 2)(r + 2) = 0

Reorder the terms:
(2 + 5r)(r + 2) = 0

Reorder the terms:
(2 + 5r)(2 + r) = 0

Multiply (2 + 5r) * (2 + r)
(2(2 + r) + 5r * (2 + r)) = 0
((2 * 2 + r * 2) + 5r * (2 + r)) = 0
((4 + 2r) + 5r * (2 + r)) = 0
(4 + 2r + (2 * 5r + r * 5r)) = 0
(4 + 2r + (10r + 5r2)) = 0

Combine like terms: 2r + 10r = 12r
(4 + 12r + 5r2) = 0

Solving
4 + 12r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + r)(2 + 5r) = 0

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

Simplifying
2 + r = 0

Solving
2 + r = 0

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

Add '-2' to each side of the equation.
2 + -2 + r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + r = 0 + -2
r = 0 + -2

Combine like terms: 0 + -2 = -2
r = -2

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

Simplifying
2 + 5r = 0

Solving
2 + 5r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5r = 0 + -2

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

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

Divide each side by '5'.
r = -0.4

Simplifying
r = -0.4
Solution
r = {-2, -0.4}