4r^2-r-28=5

Solution for 4r^2-r-28=5 equation:

Simplifying
4r2 + -1r + -28 = 5

Reorder the terms:
-28 + -1r + 4r2 = 5

Solving
-28 + -1r + 4r2 = 5

Solving for variable 'r'.

Reorder the terms:
-28 + -5 + -1r + 4r2 = 5 + -5

Combine like terms: -28 + -5 = -33
-33 + -1r + 4r2 = 5 + -5

Combine like terms: 5 + -5 = 0
-33 + -1r + 4r2 = 0

Factor a trinomial.
(-11 + -4r)(3 + -1r) = 0

Subproblem 1
Set the factor '(-11 + -4r)' equal to zero and attempt to solve:

Simplifying
-11 + -4r = 0

Solving
-11 + -4r = 0

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

Add '11' to each side of the equation.
-11 + 11 + -4r = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4r = 0 + 11
-4r = 0 + 11

Combine like terms: 0 + 11 = 11
-4r = 11

Divide each side by '-4'.
r = -2.75

Simplifying
r = -2.75
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-2.75, 3}