20r^2-15=13r

Solution for 20r^2-15=13r equation:

Simplifying
20r2 + -15 = 13r

Reorder the terms:
-15 + 20r2 = 13r

Solving
-15 + 20r2 = 13r

Solving for variable 'r'.

Reorder the terms:
-15 + -13r + 20r2 = 13r + -13r

Combine like terms: 13r + -13r = 0
-15 + -13r + 20r2 = 0

Factor a trinomial.
(-3 + -5r)(5 + -4r) = 0

Subproblem 1
Set the factor '(-3 + -5r)' equal to zero and attempt to solve:

Simplifying
-3 + -5r = 0

Solving
-3 + -5r = 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 + -5r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5r = 0 + 3
-5r = 0 + 3

Combine like terms: 0 + 3 = 3
-5r = 3

Divide each side by '-5'.
r = -0.6

Simplifying
r = -0.6
Subproblem 2
Set the factor '(5 + -4r)' equal to zero and attempt to solve:

Simplifying
5 + -4r = 0

Solving
5 + -4r = 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 + -4r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4r = 0 + -5
-4r = 0 + -5

Combine like terms: 0 + -5 = -5
-4r = -5

Divide each side by '-4'.
r = 1.25

Simplifying
r = 1.25
Solution
r = {-0.6, 1.25}