-r^2=-2r^2+2r+8

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Solution for -r^2=-2r^2+2r+8 equation: 


Simplifying
-1r2 = -2r2 + 2r + 8

Reorder the terms:
-1r2 = 8 + 2r + -2r2

Solving
-1r2 = 8 + 2r + -2r2

Solving for variable 'r'.

Reorder the terms:
-8 + -2r + -1r2 + 2r2 = 8 + 2r + -2r2 + -8 + -2r + 2r2

Combine like terms: -1r2 + 2r2 = 1r2
-8 + -2r + 1r2 = 8 + 2r + -2r2 + -8 + -2r + 2r2

Reorder the terms:
-8 + -2r + 1r2 = 8 + -8 + 2r + -2r + -2r2 + 2r2

Combine like terms: 8 + -8 = 0
-8 + -2r + 1r2 = 0 + 2r + -2r + -2r2 + 2r2
-8 + -2r + 1r2 = 2r + -2r + -2r2 + 2r2

Combine like terms: 2r + -2r = 0
-8 + -2r + 1r2 = 0 + -2r2 + 2r2
-8 + -2r + 1r2 = -2r2 + 2r2

Combine like terms: -2r2 + 2r2 = 0
-8 + -2r + 1r2 = 0

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


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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 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 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

Simplifying
r = -2

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 = {-2, 4}

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