4r^2=-21+31r

Solution for 4r^2=-21+31r equation:

Simplifying
4r2 = -21 + 31r

Solving
4r2 = -21 + 31r

Solving for variable 'r'.

Reorder the terms:
21 + -31r + 4r2 = -21 + 31r + 21 + -31r

Reorder the terms:
21 + -31r + 4r2 = -21 + 21 + 31r + -31r

Combine like terms: -21 + 21 = 0
21 + -31r + 4r2 = 0 + 31r + -31r
21 + -31r + 4r2 = 31r + -31r

Combine like terms: 31r + -31r = 0
21 + -31r + 4r2 = 0

Factor a trinomial.
(3 + -4r)(7 + -1r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {0.75, 7}