-3r^2+2r=7-9+4r+r^2

Solution for -3r^2+2r=7-9+4r+r^2 equation:

Simplifying
-3r2 + 2r = 7 + -9 + 4r + r2

Reorder the terms:
2r + -3r2 = 7 + -9 + 4r + r2

Combine like terms: 7 + -9 = -2
2r + -3r2 = -2 + 4r + r2

Solving
2r + -3r2 = -2 + 4r + r2

Solving for variable 'r'.

Reorder the terms:
2 + 2r + -4r + -3r2 + -1r2 = -2 + 4r + r2 + 2 + -4r + -1r2

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

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

Reorder the terms:
2 + -2r + -4r2 = -2 + 2 + 4r + -4r + r2 + -1r2

Combine like terms: -2 + 2 = 0
2 + -2r + -4r2 = 0 + 4r + -4r + r2 + -1r2
2 + -2r + -4r2 = 4r + -4r + r2 + -1r2

Combine like terms: 4r + -4r = 0
2 + -2r + -4r2 = 0 + r2 + -1r2
2 + -2r + -4r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
2 + -2r + -4r2 = 0

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

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

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

Simplifying
1 + -2r = 0

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

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

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

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

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

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

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

Simplifying
r = -1
Solution
r = {0.5, -1}