5r^2-10r=-5

Solution for 5r^2-10r=-5 equation:

Simplifying
5r2 + -10r = -5

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

Solving
-10r + 5r2 = -5

Solving for variable 'r'.

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

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

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -2r + r2) = 0

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1
Solution
r = {1, 1}