4r^2+31r=90

Solution for 4r^2+31r=90 equation:

Simplifying
4r2 + 31r = 90

Reorder the terms:
31r + 4r2 = 90

Solving
31r + 4r2 = 90

Solving for variable 'r'.

Reorder the terms:
-90 + 31r + 4r2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 31r + 4r2 = 0

Factor a trinomial.
(-10 + -1r)(9 + -4r) = 0

Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(9 + -4r)' equal to zero and attempt to solve:

Simplifying
9 + -4r = 0

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

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

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

Divide each side by '-4'.
r = 2.25

Simplifying
r = 2.25
Solution
r = {-10, 2.25}