7r^2-51r=-74

Solution for 7r^2-51r=-74 equation:

Simplifying
7r2 + -51r = -74

Reorder the terms:
-51r + 7r2 = -74

Solving
-51r + 7r2 = -74

Solving for variable 'r'.

Reorder the terms:
74 + -51r + 7r2 = -74 + 74

Combine like terms: -74 + 74 = 0
74 + -51r + 7r2 = 0

Factor a trinomial.
(2 + -1r)(37 + -7r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(37 + -7r)' equal to zero and attempt to solve:

Simplifying
37 + -7r = 0

Solving
37 + -7r = 0

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

Add '-37' to each side of the equation.
37 + -37 + -7r = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -7r = 0 + -37
-7r = 0 + -37

Combine like terms: 0 + -37 = -37
-7r = -37

Divide each side by '-7'.
r = 5.285714286

Simplifying
r = 5.285714286
Solution
r = {2, 5.285714286}