1+a*cosx=a^2+2a+1

Solution for 1+a*cosx=a^2+2a+1 equation:

Simplifying
1 + a * cosx = a2 + 2a + 1

Multiply a * cosx
1 + acosx = a2 + 2a + 1

Reorder the terms:
1 + acosx = 1 + 2a + a2

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

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

Reorder the terms:
acosx = 1 + -1 + 2a + a2

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

Solving
acosx = 2a + a2

Solving for variable 'a'.

Reorder the terms:
-2a + acosx + -1a2 = 2a + a2 + -2a + -1a2

Reorder the terms:
-2a + acosx + -1a2 = 2a + -2a + a2 + -1a2

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

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

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

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-2 + cosx + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + cosx + -1a = 0

Reorder the terms:
-2 + -1a + cosx = 0

Solving
-2 + -1a + cosx = 0

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

Add '2' to each side of the equation.
-2 + -1a + 2 + cosx = 0 + 2

Reorder the terms:
-2 + 2 + -1a + cosx = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a + cosx = 0 + 2
-1a + cosx = 0 + 2

Combine like terms: 0 + 2 = 2
-1a + cosx = 2

Add '-1cosx' to each side of the equation.
-1a + cosx + -1cosx = 2 + -1cosx

Combine like terms: cosx + -1cosx = 0
-1a + 0 = 2 + -1cosx
-1a = 2 + -1cosx

Divide each side by '-1'.
a = -2 + cosx

Simplifying
a = -2 + cosx
Solution
a = {0, -2 + cosx}