7r^2+14r-61=-5

Solution for 7r^2+14r-61=-5 equation:

Simplifying
7r2 + 14r + -61 = -5

Reorder the terms:
-61 + 14r + 7r2 = -5

Solving
-61 + 14r + 7r2 = -5

Solving for variable 'r'.

Reorder the terms:
-61 + 5 + 14r + 7r2 = -5 + 5

Combine like terms: -61 + 5 = -56
-56 + 14r + 7r2 = -5 + 5

Combine like terms: -5 + 5 = 0
-56 + 14r + 7r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + 2r + r2) = 0

Factor a trinomial.
7((-4 + -1r)(2 + -1r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-4, 2}