4r^2-35r-9=0

Solution for 4r^2-35r-9=0 equation:

Simplifying
4r2 + -35r + -9 = 0

Reorder the terms:
-9 + -35r + 4r2 = 0

Solving
-9 + -35r + 4r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -4r)(9 + -1r) = 0

Subproblem 1
Set the factor '(-1 + -4r)' equal to zero and attempt to solve:

Simplifying
-1 + -4r = 0

Solving
-1 + -4r = 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 + -4r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4r = 0 + 1
-4r = 0 + 1

Combine like terms: 0 + 1 = 1
-4r = 1

Divide each side by '-4'.
r = -0.25

Simplifying
r = -0.25
Subproblem 2
Set the factor '(9 + -1r)' equal to zero and attempt to solve:

Simplifying
9 + -1r = 0

Solving
9 + -1r = 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 + -1r = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1r = 0 + -9
-1r = 0 + -9

Combine like terms: 0 + -9 = -9
-1r = -9

Divide each side by '-1'.
r = 9

Simplifying
r = 9
Solution
r = {-0.25, 9}