1+(1+r)(1+r)=2

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

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

Multiply (1 + r) * (1 + r)
1 + (1(1 + r) + r(1 + r)) = 2
1 + ((1 * 1 + r * 1) + r(1 + r)) = 2
1 + ((1 + 1r) + r(1 + r)) = 2
1 + (1 + 1r + (1 * r + r * r)) = 2
1 + (1 + 1r + (1r + r2)) = 2

Combine like terms: 1r + 1r = 2r
1 + (1 + 2r + r2) = 2

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

Add '-2' to each side of the equation.
2 + 2r + -2 + r2 = 2 + -2

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

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

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

Solving
2r + r2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

Move all terms containing r to the left, all other terms to the right.

Simplifying
r = 0
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

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

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

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

Simplifying
r = -2
Solution
r = {0, -2}