5r(r+6)=10(r-2)

Solution for 5r(r+6)=10(r-2) equation:

Simplifying
5r(r + 6) = 10(r + -2)

Reorder the terms:
5r(6 + r) = 10(r + -2)
(6 * 5r + r * 5r) = 10(r + -2)
(30r + 5r2) = 10(r + -2)

Reorder the terms:
30r + 5r2 = 10(-2 + r)
30r + 5r2 = (-2 * 10 + r * 10)
30r + 5r2 = (-20 + 10r)

Solving
30r + 5r2 = -20 + 10r

Solving for variable 'r'.

Reorder the terms:
20 + 30r + -10r + 5r2 = -20 + 10r + 20 + -10r

Combine like terms: 30r + -10r = 20r
20 + 20r + 5r2 = -20 + 10r + 20 + -10r

Reorder the terms:
20 + 20r + 5r2 = -20 + 20 + 10r + -10r

Combine like terms: -20 + 20 = 0
20 + 20r + 5r2 = 0 + 10r + -10r
20 + 20r + 5r2 = 10r + -10r

Combine like terms: 10r + -10r = 0
20 + 20r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + 4r + r2) = 0

Factor a trinomial.
5((2 + r)(2 + r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

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

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

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

Simplifying
2 + r = 0

Solving
2 + r = 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 + r = 0 + -2

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

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

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