6r^2+8r-20=5r^2

Solution for 6r^2+8r-20=5r^2 equation:

Simplifying
6r2 + 8r + -20 = 5r2

Reorder the terms:
-20 + 8r + 6r2 = 5r2

Solving
-20 + 8r + 6r2 = 5r2

Solving for variable 'r'.

Combine like terms: 6r2 + -5r2 = 1r2
-20 + 8r + 1r2 = 5r2 + -5r2

Combine like terms: 5r2 + -5r2 = 0
-20 + 8r + 1r2 = 0

Factor a trinomial.
(-10 + -1r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-10 + -1r)' equal to zero and attempt to solve:

Simplifying
-10 + -1r = 0

Solving
-10 + -1r = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1r = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1r = 0 + 10
-1r = 0 + 10

Combine like terms: 0 + 10 = 10
-1r = 10

Divide each side by '-1'.
r = -10

Simplifying
r = -10
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-10, 2}