4r^2-12r-31=-4

Solution for 4r^2-12r-31=-4 equation:

Simplifying
4r2 + -12r + -31 = -4

Reorder the terms:
-31 + -12r + 4r2 = -4

Solving
-31 + -12r + 4r2 = -4

Solving for variable 'r'.

Reorder the terms:
-31 + 4 + -12r + 4r2 = -4 + 4

Combine like terms: -31 + 4 = -27
-27 + -12r + 4r2 = -4 + 4

Combine like terms: -4 + 4 = 0
-27 + -12r + 4r2 = 0

Factor a trinomial.
(-3 + -2r)(9 + -2r) = 0

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

Simplifying
-3 + -2r = 0

Solving
-3 + -2r = 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 + -2r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2r = 0 + 3
-2r = 0 + 3

Combine like terms: 0 + 3 = 3
-2r = 3

Divide each side by '-2'.
r = -1.5

Simplifying
r = -1.5
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 = {-1.5, 4.5}