2r(2r+2)+(3r+1)=r-1

Solution for 2r(2r+2)+(3r+1)=r-1 equation:

Simplifying
2r(2r + 2) + (3r + 1) = r + -1

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

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

Remove parenthesis around (1 + 3r)
4r + 4r2 + 1 + 3r = r + -1

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

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

Reorder the terms:
1 + 7r + 4r2 = -1 + r

Solving
1 + 7r + 4r2 = -1 + r

Solving for variable 'r'.

Reorder the terms:
1 + 1 + 7r + -1r + 4r2 = -1 + r + 1 + -1r

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

Combine like terms: 7r + -1r = 6r
2 + 6r + 4r2 = -1 + r + 1 + -1r

Reorder the terms:
2 + 6r + 4r2 = -1 + 1 + r + -1r

Combine like terms: -1 + 1 = 0
2 + 6r + 4r2 = 0 + r + -1r
2 + 6r + 4r2 = r + -1r

Combine like terms: r + -1r = 0
2 + 6r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 3r + 2r2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
r = {-1, -0.5}