-2r^2+114=-7r

Solution for -2r^2+114=-7r equation:

Simplifying
-2r2 + 114 = -7r

Reorder the terms:
114 + -2r2 = -7r

Solving
114 + -2r2 = -7r

Solving for variable 'r'.

Reorder the terms:
114 + 7r + -2r2 = -7r + 7r

Combine like terms: -7r + 7r = 0
114 + 7r + -2r2 = 0

Factor a trinomial.
(19 + -2r)(6 + r) = 0

Subproblem 1
Set the factor '(19 + -2r)' equal to zero and attempt to solve:

Simplifying
19 + -2r = 0

Solving
19 + -2r = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2r = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2r = 0 + -19
-2r = 0 + -19

Combine like terms: 0 + -19 = -19
-2r = -19

Divide each side by '-2'.
r = 9.5

Simplifying
r = 9.5
Subproblem 2
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {9.5, -6}