56r^2-17r=3

Solution for 56r^2-17r=3 equation:

Simplifying
56r2 + -17r = 3

Reorder the terms:
-17r + 56r2 = 3

Solving
-17r + 56r2 = 3

Solving for variable 'r'.

Reorder the terms:
-3 + -17r + 56r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -17r + 56r2 = 0

Factor a trinomial.
(-1 + -8r)(3 + -7r) = 0

Subproblem 1
Set the factor '(-1 + -8r)' equal to zero and attempt to solve:

Simplifying
-1 + -8r = 0

Solving
-1 + -8r = 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 + -8r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8r = 0 + 1
-8r = 0 + 1

Combine like terms: 0 + 1 = 1
-8r = 1

Divide each side by '-8'.
r = -0.125

Simplifying
r = -0.125
Subproblem 2
Set the factor '(3 + -7r)' equal to zero and attempt to solve:

Simplifying
3 + -7r = 0

Solving
3 + -7r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7r = 0 + -3
-7r = 0 + -3

Combine like terms: 0 + -3 = -3
-7r = -3

Divide each side by '-7'.
r = 0.4285714286

Simplifying
r = 0.4285714286
Solution
r = {-0.125, 0.4285714286}