245r^2-373r+112=5r

Solution for 245r^2-373r+112=5r equation:

Simplifying
245r2 + -373r + 112 = 5r

Reorder the terms:
112 + -373r + 245r2 = 5r

Solving
112 + -373r + 245r2 = 5r

Solving for variable 'r'.

Reorder the terms:
112 + -373r + -5r + 245r2 = 5r + -5r

Combine like terms: -373r + -5r = -378r
112 + -378r + 245r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
112 + -378r + 245r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(16 + -54r + 35r2) = 0

Factor a trinomial.
7((2 + -5r)(8 + -7r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(2 + -5r)' equal to zero and attempt to solve:

Simplifying
2 + -5r = 0

Solving
2 + -5r = 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 + -5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5r = 0 + -2
-5r = 0 + -2

Combine like terms: 0 + -2 = -2
-5r = -2

Divide each side by '-5'.
r = 0.4

Simplifying
r = 0.4
Subproblem 2
Set the factor '(8 + -7r)' equal to zero and attempt to solve:

Simplifying
8 + -7r = 0

Solving
8 + -7r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7r = 0 + -8
-7r = 0 + -8

Combine like terms: 0 + -8 = -8
-7r = -8

Divide each side by '-7'.
r = 1.142857143

Simplifying
r = 1.142857143
Solution
r = {0.4, 1.142857143}