5r^2+20r+24=9

Solution for 5r^2+20r+24=9 equation:

Simplifying
5r2 + 20r + 24 = 9

Reorder the terms:
24 + 20r + 5r2 = 9

Solving
24 + 20r + 5r2 = 9

Solving for variable 'r'.

Reorder the terms:
24 + -9 + 20r + 5r2 = 9 + -9

Combine like terms: 24 + -9 = 15
15 + 20r + 5r2 = 9 + -9

Combine like terms: 9 + -9 = 0
15 + 20r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + 4r + r2) = 0

Factor a trinomial.
5((3 + r)(1 + r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

Solving
3 + r = 0

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

Add '-3' to each side of the equation.
3 + -3 + r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + r = 0 + -3
r = 0 + -3

Combine like terms: 0 + -3 = -3
r = -3

Simplifying
r = -3
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

Solving
1 + r = 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 + r = 0 + -1

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

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

Simplifying
r = -1
Solution
r = {-3, -1}