7r^2-14r-31=-10

Solution for 7r^2-14r-31=-10 equation:

Simplifying
7r2 + -14r + -31 = -10

Reorder the terms:
-31 + -14r + 7r2 = -10

Solving
-31 + -14r + 7r2 = -10

Solving for variable 'r'.

Reorder the terms:
-31 + 10 + -14r + 7r2 = -10 + 10

Combine like terms: -31 + 10 = -21
-21 + -14r + 7r2 = -10 + 10

Combine like terms: -10 + 10 = 0
-21 + -14r + 7r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + -2r + r2) = 0

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

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

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

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

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

Simplifying
r = -1
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 = {-1, 3}