56r^2-19r=15

Solution for 56r^2-19r=15 equation:

Simplifying
56r2 + -19r = 15

Reorder the terms:
-19r + 56r2 = 15

Solving
-19r + 56r2 = 15

Solving for variable 'r'.

Reorder the terms:
-15 + -19r + 56r2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -19r + 56r2 = 0

Factor a trinomial.
(-3 + -8r)(5 + -7r) = 0

Subproblem 1
Set the factor '(-3 + -8r)' equal to zero and attempt to solve:

Simplifying
-3 + -8r = 0

Solving
-3 + -8r = 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 + -8r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8r = 0 + 3
-8r = 0 + 3

Combine like terms: 0 + 3 = 3
-8r = 3

Divide each side by '-8'.
r = -0.375

Simplifying
r = -0.375
Subproblem 2
Set the factor '(5 + -7r)' equal to zero and attempt to solve:

Simplifying
5 + -7r = 0

Solving
5 + -7r = 0

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

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

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

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

Divide each side by '-7'.
r = 0.7142857143

Simplifying
r = 0.7142857143
Solution
r = {-0.375, 0.7142857143}