10r^2-19r+7=0

Solution for 10r^2-19r+7=0 equation:

Simplifying
10r2 + -19r + 7 = 0

Reorder the terms:
7 + -19r + 10r2 = 0

Solving
7 + -19r + 10r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -2r)(7 + -5r) = 0

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

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

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

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

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 2
Set the factor '(7 + -5r)' equal to zero and attempt to solve:

Simplifying
7 + -5r = 0

Solving
7 + -5r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5r = 0 + -7
-5r = 0 + -7

Combine like terms: 0 + -7 = -7
-5r = -7

Divide each side by '-5'.
r = 1.4

Simplifying
r = 1.4
Solution
r = {0.5, 1.4}