2r^2-40=-2r

Solution for 2r^2-40=-2r equation:

Simplifying
2r2 + -40 = -2r

Reorder the terms:
-40 + 2r2 = -2r

Solving
-40 + 2r2 = -2r

Solving for variable 'r'.

Reorder the terms:
-40 + 2r + 2r2 = -2r + 2r

Combine like terms: -2r + 2r = 0
-40 + 2r + 2r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + r + r2) = 0

Factor a trinomial.
2((-5 + -1r)(4 + -1r)) = 0

Ignore the factor 2.
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 '(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
Solution
r = {-5, 4}