4r^2-16r-9=0

Solution for 4r^2-16r-9=0 equation:

Simplifying
4r2 + -16r + -9 = 0

Reorder the terms:
-9 + -16r + 4r2 = 0

Solving
-9 + -16r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -2r)(9 + -2r) = 0

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

Simplifying
-1 + -2r = 0

Solving
-1 + -2r = 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 + -2r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2r = 0 + 1
-2r = 0 + 1

Combine like terms: 0 + 1 = 1
-2r = 1

Divide each side by '-2'.
r = -0.5

Simplifying
r = -0.5
Subproblem 2
Set the factor '(9 + -2r)' equal to zero and attempt to solve:

Simplifying
9 + -2r = 0

Solving
9 + -2r = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2r = 0 + -9
-2r = 0 + -9

Combine like terms: 0 + -9 = -9
-2r = -9

Divide each side by '-2'.
r = 4.5

Simplifying
r = 4.5
Solution
r = {-0.5, 4.5}