2r(2r-10)=200

Solution for 2r(2r-10)=200 equation:

Simplifying
2r(2r + -10) = 200

Reorder the terms:
2r(-10 + 2r) = 200
(-10 * 2r + 2r * 2r) = 200
(-20r + 4r2) = 200

Solving
-20r + 4r2 = 200

Solving for variable 'r'.

Reorder the terms:
-200 + -20r + 4r2 = 200 + -200

Combine like terms: 200 + -200 = 0
-200 + -20r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-50 + -5r + r2) = 0

Factor a trinomial.
4((-5 + -1r)(10 + -1r)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
r = {-5, 10}