r^2+6r=20+7r

Solution for r^2+6r=20+7r equation:

Simplifying
r2 + 6r = 20 + 7r

Reorder the terms:
6r + r2 = 20 + 7r

Solving
6r + r2 = 20 + 7r

Solving for variable 'r'.

Reorder the terms:
-20 + 6r + -7r + r2 = 20 + 7r + -20 + -7r

Combine like terms: 6r + -7r = -1r
-20 + -1r + r2 = 20 + 7r + -20 + -7r

Reorder the terms:
-20 + -1r + r2 = 20 + -20 + 7r + -7r

Combine like terms: 20 + -20 = 0
-20 + -1r + r2 = 0 + 7r + -7r
-20 + -1r + r2 = 7r + -7r

Combine like terms: 7r + -7r = 0
-20 + -1r + r2 = 0

Factor a trinomial.
(-4 + -1r)(5 + -1r) = 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 '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-4, 5}