a+r=a^2+2ar+a+2r

Solution for a+r=a^2+2ar+a+2r equation:

Simplifying
a + r = a2 + 2ar + a + 2r

Reorder the terms:
a + r = a + 2ar + a2 + 2r

Add '-1a' to each side of the equation.
a + -1a + r = a + 2ar + a2 + -1a + 2r

Combine like terms: a + -1a = 0
0 + r = a + 2ar + a2 + -1a + 2r
r = a + 2ar + a2 + -1a + 2r

Reorder the terms:
r = a + -1a + 2ar + a2 + 2r

Combine like terms: a + -1a = 0
r = 0 + 2ar + a2 + 2r
r = 2ar + a2 + 2r

Solving
r = 2ar + a2 + 2r

Solving for variable 'r'.

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

Add '-2ar' to each side of the equation.
-2ar + r = 2ar + a2 + -2ar + 2r

Reorder the terms:
-2ar + r = 2ar + -2ar + a2 + 2r

Combine like terms: 2ar + -2ar = 0
-2ar + r = 0 + a2 + 2r
-2ar + r = a2 + 2r

Add '-2r' to each side of the equation.
-2ar + r + -2r = a2 + 2r + -2r

Combine like terms: r + -2r = -1r
-2ar + -1r = a2 + 2r + -2r

Combine like terms: 2r + -2r = 0
-2ar + -1r = a2 + 0
-2ar + -1r = a2

Reorder the terms:
-2ar + -1a2 + -1r = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-2ar + -1a2 + -1r = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2ar + a2 + r) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2ar + a2 + r)' equal to zero and attempt to solve:

Simplifying
2ar + a2 + r = 0

Solving
2ar + a2 + r = 0

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

Add '-1a2' to each side of the equation.
2ar + a2 + -1a2 + r = 0 + -1a2

Combine like terms: a2 + -1a2 = 0
2ar + 0 + r = 0 + -1a2
2ar + r = 0 + -1a2
Remove the zero:
2ar + r = -1a2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.