2r^2-14r=88

Solution for 2r^2-14r=88 equation:

Simplifying
2r2 + -14r = 88

Reorder the terms:
-14r + 2r2 = 88

Solving
-14r + 2r2 = 88

Solving for variable 'r'.

Reorder the terms:
-88 + -14r + 2r2 = 88 + -88

Combine like terms: 88 + -88 = 0
-88 + -14r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-44 + -7r + r2) = 0

Factor a trinomial.
2((-4 + -1r)(11 + -1r)) = 0

Ignore the factor 2.
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 '(11 + -1r)' equal to zero and attempt to solve:

Simplifying
11 + -1r = 0

Solving
11 + -1r = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1r = 0 + -11
-1r = 0 + -11

Combine like terms: 0 + -11 = -11
-1r = -11

Divide each side by '-1'.
r = 11

Simplifying
r = 11
Solution
r = {-4, 11}