r^2+6r=2r(2)(r+6)

Solution for r^2+6r=2r(2)(r+6) equation:

Simplifying
r2 + 6r = 2r(2)(r + 6)

Reorder the terms:
6r + r2 = 2r(2)(r + 6)

Reorder the terms:
6r + r2 = 2r * 2(6 + r)

Reorder the terms for easier multiplication:
6r + r2 = 2 * 2r(6 + r)

Multiply 2 * 2
6r + r2 = 4r(6 + r)
6r + r2 = (6 * 4r + r * 4r)
6r + r2 = (24r + 4r2)

Solving
6r + r2 = 24r + 4r2

Solving for variable 'r'.

Reorder the terms:
6r + -24r + r2 + -4r2 = 24r + 4r2 + -24r + -4r2

Combine like terms: 6r + -24r = -18r
-18r + r2 + -4r2 = 24r + 4r2 + -24r + -4r2

Combine like terms: r2 + -4r2 = -3r2
-18r + -3r2 = 24r + 4r2 + -24r + -4r2

Reorder the terms:
-18r + -3r2 = 24r + -24r + 4r2 + -4r2

Combine like terms: 24r + -24r = 0
-18r + -3r2 = 0 + 4r2 + -4r2
-18r + -3r2 = 4r2 + -4r2

Combine like terms: 4r2 + -4r2 = 0
-18r + -3r2 = 0

Factor out the Greatest Common Factor (GCF), '-3r'.
-3r(6 + r) = 0

Ignore the factor -3.
Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
Solution
r = {0, -6}