3r^2+16r-31=4

Solution for 3r^2+16r-31=4 equation:

Simplifying
3r2 + 16r + -31 = 4

Reorder the terms:
-31 + 16r + 3r2 = 4

Solving
-31 + 16r + 3r2 = 4

Solving for variable 'r'.

Reorder the terms:
-31 + -4 + 16r + 3r2 = 4 + -4

Combine like terms: -31 + -4 = -35
-35 + 16r + 3r2 = 4 + -4

Combine like terms: 4 + -4 = 0
-35 + 16r + 3r2 = 0

Factor a trinomial.
(-7 + -1r)(5 + -3r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

Solving
5 + -3r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3r = 0 + -5
-3r = 0 + -5

Combine like terms: 0 + -5 = -5
-3r = -5

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {-7, 1.666666667}