=4r^2+15r+9

Solution for =4r^2+15r+9 equation:

Simplifying
0 = 4r2 + 15r + 9

Reorder the terms:
0 = 9 + 15r + 4r2

Solving
0 = 9 + 15r + 4r2

Solving for variable 'r'.

Combine like terms: 0 + -9 = -9
-9 + -15r + -4r2 = 9 + 15r + 4r2 + -9 + -15r + -4r2

Reorder the terms:
-9 + -15r + -4r2 = 9 + -9 + 15r + -15r + 4r2 + -4r2

Combine like terms: 9 + -9 = 0
-9 + -15r + -4r2 = 0 + 15r + -15r + 4r2 + -4r2
-9 + -15r + -4r2 = 15r + -15r + 4r2 + -4r2

Combine like terms: 15r + -15r = 0
-9 + -15r + -4r2 = 0 + 4r2 + -4r2
-9 + -15r + -4r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
-9 + -15r + -4r2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 15r + 4r2) = 0

Factor a trinomial.
-1((3 + r)(3 + 4r)) = 0

Ignore the factor -1.
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 '(3 + 4r)' equal to zero and attempt to solve:

Simplifying
3 + 4r = 0

Solving
3 + 4r = 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 + 4r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4r = 0 + -3
4r = 0 + -3

Combine like terms: 0 + -3 = -3
4r = -3

Divide each side by '4'.
r = -0.75

Simplifying
r = -0.75
Solution
r = {-3, -0.75}