5r^2+6r-56=0

Solution for 5r^2+6r-56=0 equation:

Simplifying
5r2 + 6r + -56 = 0

Reorder the terms:
-56 + 6r + 5r2 = 0

Solving
-56 + 6r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-4 + -1r)(14 + -5r) = 0

Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve:

Simplifying
-4 + -1r = 0

Solving
-4 + -1r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1r = 0 + 4
-1r = 0 + 4

Combine like terms: 0 + 4 = 4
-1r = 4

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(14 + -5r)' equal to zero and attempt to solve:

Simplifying
14 + -5r = 0

Solving
14 + -5r = 0

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

Add '-14' to each side of the equation.
14 + -14 + -5r = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -5r = 0 + -14
-5r = 0 + -14

Combine like terms: 0 + -14 = -14
-5r = -14

Divide each side by '-5'.
r = 2.8

Simplifying
r = 2.8
Solution
r = {-4, 2.8}