4r^2+24r-45=0

Solution for 4r^2+24r-45=0 equation:

Simplifying
4r2 + 24r + -45 = 0

Reorder the terms:
-45 + 24r + 4r2 = 0

Solving
-45 + 24r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-15 + -2r)(3 + -2r) = 0

Subproblem 1
Set the factor '(-15 + -2r)' equal to zero and attempt to solve:

Simplifying
-15 + -2r = 0

Solving
-15 + -2r = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2r = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2r = 0 + 15
-2r = 0 + 15

Combine like terms: 0 + 15 = 15
-2r = 15

Divide each side by '-2'.
r = -7.5

Simplifying
r = -7.5
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-7.5, 1.5}