-r+3=7-3r-2r^2

Solution for -r+3=7-3r-2r^2 equation:

Simplifying
-1r + 3 = 7 + -3r + -2r2

Reorder the terms:
3 + -1r = 7 + -3r + -2r2

Solving
3 + -1r = 7 + -3r + -2r2

Solving for variable 'r'.

Reorder the terms:
3 + -7 + -1r + 3r + 2r2 = 7 + -3r + -2r2 + -7 + 3r + 2r2

Combine like terms: 3 + -7 = -4
-4 + -1r + 3r + 2r2 = 7 + -3r + -2r2 + -7 + 3r + 2r2

Combine like terms: -1r + 3r = 2r
-4 + 2r + 2r2 = 7 + -3r + -2r2 + -7 + 3r + 2r2

Reorder the terms:
-4 + 2r + 2r2 = 7 + -7 + -3r + 3r + -2r2 + 2r2

Combine like terms: 7 + -7 = 0
-4 + 2r + 2r2 = 0 + -3r + 3r + -2r2 + 2r2
-4 + 2r + 2r2 = -3r + 3r + -2r2 + 2r2

Combine like terms: -3r + 3r = 0
-4 + 2r + 2r2 = 0 + -2r2 + 2r2
-4 + 2r + 2r2 = -2r2 + 2r2

Combine like terms: -2r2 + 2r2 = 0
-4 + 2r + 2r2 = 0

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

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

Ignore the factor 2.
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 '(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 = {-2, 1}